1
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Holmes IA, Durso AM, Myers CR, Hendry TA. Changes in capture availability due to infection can lead to detectable biases in population-level infectious disease parameters. PeerJ 2024; 12:e16910. [PMID: 38436008 PMCID: PMC10909344 DOI: 10.7717/peerj.16910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 01/17/2024] [Indexed: 03/05/2024] Open
Abstract
Correctly identifying the strength of selection that parasites impose on hosts is key to predicting epidemiological and evolutionary outcomes of host-parasite interactions. However, behavioral changes due to infection can alter the capture probability of infected hosts and thereby make selection difficult to estimate by standard sampling techniques. Mark-recapture approaches, which allow researchers to determine if some groups in a population are less likely to be captured than others, can be used to identify infection-driven capture biases. If a metric of interest directly compares infected and uninfected populations, calculated detection probabilities for both groups may be useful in identifying bias. Here, we use an individual-based simulation to test whether changes in capture rate due to infection can alter estimates of three key metrics: 1) reduction in the reproductive success of infected parents relative to uninfected parents, 2) the relative risk of infection for susceptible genotypes compared to resistant genotypes, and 3) changes in allele frequencies between generations. We explore the direction and underlying causes of the biases that emerge from these simulations. Finally, we argue that short series of mark-recapture sampling bouts, potentially implemented in under a week, can yield key data on detection bias due to infection while not adding a significantly higher burden to disease ecology studies.
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Affiliation(s)
- Iris A. Holmes
- Department of Microbiology, Cornell University, Ithaca, NY, United States
- Cornell Institute of Host Microbe Interactions and Disease, Cornell University, Ithaca, NY, United States
| | - Andrew M. Durso
- Department of Biological Sciences, Florida Gulf Coast University, Ft. Myers, FL, USA
| | - Christopher R. Myers
- Center for Advanced Computing & Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, United States
| | - Tory A. Hendry
- Department of Microbiology, Cornell University, Ithaca, NY, United States
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2
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Bartesaghi P, Clemente GP, Grassi R. A novel self-adaptive SIS model based on the mutual interaction between a graph and its line graph. CHAOS (WOODBURY, N.Y.) 2024; 34:023117. [PMID: 38363959 DOI: 10.1063/5.0186658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 01/23/2024] [Indexed: 02/18/2024]
Abstract
We propose a new paradigm to design a network-based self-adaptive epidemic model that relies on the interplay between the network and its line graph. We implement this proposal on a susceptible-infected-susceptible model in which both nodes and edges are considered susceptible and their respective probabilities of being infected result in a real-time re-modulation of the weights of both the graph and its line graph. The new model can be considered as an appropriate perturbation of the standard susceptible-infected-susceptible model, and the coupling between the graph and its line graph is interpreted as a reinforcement factor that fosters diffusion through a continuous adjustment of the parameters involved. We study the existence and stability conditions of the endemic and disease-free states for general network topologies. Moreover, we introduce, through the asymptotic values in the endemic steady states, a new type of eigenvector centrality where the score of a node depends on both the neighboring nodes and the edges connected to it. We also investigate the properties of this new model on some specific synthetic graphs, such as cycle, regular, and star graphs. Finally, we perform a series of numerical simulations and prove their effectiveness in capturing some empirical evidence on behavioral adoption mechanisms.
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Affiliation(s)
- Paolo Bartesaghi
- Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy
| | - Gian Paolo Clemente
- Dipartimento di Matematica per le Scienze Economiche, Finanziarie ed Attuariali, Universitá Cattolica del Sacro Cuore di Milano, Largo Gemelli 1, 20123 Milano, Italy
| | - Rosanna Grassi
- Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy
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3
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Parag KV, Obolski U. Risk averse reproduction numbers improve resurgence detection. PLoS Comput Biol 2023; 19:e1011332. [PMID: 37471464 PMCID: PMC10393178 DOI: 10.1371/journal.pcbi.1011332] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2022] [Accepted: 07/06/2023] [Indexed: 07/22/2023] Open
Abstract
The effective reproduction number R is a prominent statistic for inferring the transmissibility of infectious diseases and effectiveness of interventions. R purportedly provides an easy-to-interpret threshold for deducing whether an epidemic will grow (R>1) or decline (R<1). We posit that this interpretation can be misleading and statistically overconfident when applied to infections accumulated from groups featuring heterogeneous dynamics. These groups may be delineated by geography, infectiousness or sociodemographic factors. In these settings, R implicitly weights the dynamics of the groups by their number of circulating infections. We find that this weighting can cause delayed detection of outbreak resurgence and premature signalling of epidemic control because it underrepresents the risks from highly transmissible groups. Applying E-optimal experimental design theory, we develop a weighting algorithm to minimise these issues, yielding the risk averse reproduction number E. Using simulations, analytic approaches and real-world COVID-19 data stratified at the city and district level, we show that E meaningfully summarises transmission dynamics across groups, balancing bias from the averaging underlying R with variance from directly using local group estimates. An E>1generates timely resurgence signals (upweighting risky groups), while an E<1ensures local outbreaks are under control. We propose E as an alternative to R for informing policy and assessing transmissibility at large scales (e.g., state-wide or nationally), where R is commonly computed but well-mixed or homogeneity assumptions break down.
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Affiliation(s)
- Kris V Parag
- MRC Centre for Global Infectious Disease Analysis, Imperial College London, London, United Kingdom
| | - Uri Obolski
- School of Public Health, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
- Porter School of the Environment and Earth Sciences, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
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4
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Pardo-Araujo M, García-García D, Alonso D, Bartumeus F. Epidemic thresholds and human mobility. Sci Rep 2023; 13:11409. [PMID: 37452118 PMCID: PMC10349094 DOI: 10.1038/s41598-023-38395-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 07/07/2023] [Indexed: 07/18/2023] Open
Abstract
A comprehensive view of disease epidemics demands a deep understanding of the complex interplay between human behaviour and infectious diseases. Here, we propose a flexible modelling framework that brings conclusions about the influence of human mobility and disease transmission on early epidemic growth, with applicability in outbreak preparedness. We use random matrix theory to compute an epidemic threshold, equivalent to the basic reproduction number [Formula: see text], for a SIR metapopulation model. The model includes both systematic and random features of human mobility. Variations in disease transmission rates, mobility modes (i.e. commuting and migration), and connectivity strengths determine the threshold value and whether or not a disease may potentially establish in the population, as well as the local incidence distribution.
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Affiliation(s)
| | - David García-García
- Consorcio de Investigación Biomédica en Red de Epidemiología y Salud Pública (CIBERESP), Madrid, Spain.
- Centro Nacional de Epidemiología (CNE-ISCIII), Madrid, Spain.
| | - David Alonso
- Centre d'Estudis Avançats de Blanes (CEAB-CSIC), Blanes, Spain
| | - Frederic Bartumeus
- Centre d'Estudis Avançats de Blanes (CEAB-CSIC), Blanes, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
- Centre de Recerca Ecològica i Aplicacions Forestals (CREAF), Barcelona, Spain
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5
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Iyer S, Karrer B, Citron DT, Kooti F, Maas P, Wang Z, Giraudy E, Medhat A, Dow PA, Pompe A. Large-scale measurement of aggregate human colocation patterns for epidemiological modeling. Epidemics 2023; 42:100663. [PMID: 36724622 DOI: 10.1016/j.epidem.2022.100663] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Revised: 12/06/2022] [Accepted: 12/20/2022] [Indexed: 01/12/2023] Open
Abstract
To understand and model public health emergencies, epidemiologists need data that describes how humans are moving and interacting across physical space. Such data has traditionally been difficult for researchers to obtain with the temporal resolution and geographic breadth that is needed to study, for example, a global pandemic. This paper describes Colocation Maps, which are spatial network datasets that have been developed within Meta's Data For Good program. These Maps estimate how often people from different regions are colocated: in particular, for a pair of geographic regions x and y, these Maps estimate the rate at which a randomly chosen person from x and a randomly chosen person from y are simultaneously located in the same place during a randomly chosen minute in a given week. These datasets are well suited to parametrize metapopulation models of disease spread or to measure temporal changes in interactions between people from different regions; indeed, they have already been used for both of these purposes during the COVID-19 pandemic. In this paper, we show how Colocation Maps differ from existing data sources, describe how the datasets are built, provide examples of their use in compartmental modeling, and summarize ideas for further development of these and related datasets. Among the findings of this study, we observe that a pair of regions can exhibit high colocation despite few people moving between those regions. Additionally, for the purposes of clarifying how to interpret and utilize Colocation Maps, we scrutinize the Maps' built-in assumptions about representativeness and contact heterogeneity.
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Affiliation(s)
- Shankar Iyer
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States.
| | - Brian Karrer
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States
| | | | - Farshad Kooti
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States
| | - Paige Maas
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States
| | - Zeyu Wang
- Department of Economics, Stanford University, 579 Jane Stanford Way, Stanford, CA 94305, United States
| | | | - Ahmed Medhat
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States
| | - P Alex Dow
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States
| | - Alex Pompe
- Meta, 1 Hacker Way, Menlo Park, CA 94025, United States
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6
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Saucedo O, Tien JH. Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks. Infect Dis Model 2022; 7:742-760. [DOI: 10.1016/j.idm.2022.10.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 09/04/2022] [Accepted: 10/26/2022] [Indexed: 11/06/2022] Open
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7
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Ansari M, Soriano-Paños D, Ghoshal G, White AD. Inferring spatial source of disease outbreaks using maximum entropy. Phys Rev E 2022; 106:014306. [PMID: 35974607 DOI: 10.1103/physreve.106.014306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 06/29/2022] [Indexed: 06/15/2023]
Abstract
Mathematical modeling of disease outbreaks can infer the future trajectory of an epidemic, allowing for making more informed policy decisions. Another task is inferring the origin of a disease, which is relatively difficult with current mathematical models. Such frameworks, across varying levels of complexity, are typically sensitive to input data on epidemic parameters, case counts, and mortality rates, which are generally noisy and incomplete. To alleviate these limitations, we propose a maximum entropy framework that fits epidemiological models, provides calibrated infection origin probabilities, and is robust to noise due to a prior belief model. Maximum entropy is agnostic to the parameters or model structure used and allows for flexible use when faced with sparse data conditions and incomplete knowledge in the dynamical phase of disease-spread, providing for more reliable modeling at early stages of outbreaks. We evaluate the performance of our model by predicting future disease trajectories based on simulated epidemiological data in synthetic graph networks and the real mobility network of New York State. In addition, unlike existing approaches, we demonstrate that the method can be used to infer the origin of the outbreak with accurate confidence. Indeed, despite the prevalent belief on the feasibility of contact-tracing being limited to the initial stages of an outbreak, we report the possibility of reconstructing early disease dynamics, including the epidemic seed, at advanced stages.
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Affiliation(s)
- Mehrad Ansari
- Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, USA
| | - David Soriano-Paños
- Instituto Gulbenkian de Ciência (IGC), Oeiras 2780-156, Portugal
- GOTHAM Lab, Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, E-50009 Zaragoza, Spain
| | - Gourab Ghoshal
- Department of Physics and Astronomy and Computer Science, University of Rochester, Rochester, New York 14627, USA
| | - Andrew D White
- Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, USA
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8
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Marion G, Hadley L, Isham V, Mollison D, Panovska-Griffiths J, Pellis L, Tomba GS, Scarabel F, Swallow B, Trapman P, Villela D. Modelling: Understanding pandemics and how to control them. Epidemics 2022; 39:100588. [PMID: 35679714 DOI: 10.1016/j.epidem.2022.100588] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Revised: 03/22/2022] [Accepted: 05/26/2022] [Indexed: 12/11/2022] Open
Abstract
New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.
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Affiliation(s)
- Glenn Marion
- Biomathematics and Statistics Scotland, Edinburgh, UK; Scottish COVID-19 Response Consortium, UK.
| | - Liza Hadley
- Disease Dynamics Unit, Department of Veterinary Medicine, University of Cambridge, UK
| | - Valerie Isham
- Department of Statistical Science, University College London, UK
| | - Denis Mollison
- Department of Actuarial Mathematics and Statistics, Heriot-Watt University, UK
| | - Jasmina Panovska-Griffiths
- The Big Data Institute, Nuffield Department of Medicine, University of Oxford, Oxford, UK; The Queen's College, Oxford University, UK
| | - Lorenzo Pellis
- Department of Mathematics, University of Manchester, UK; The Alan Turing Institute, London, UK; Joint UNIversities Pandemic and Epidemiological Research, UK
| | | | - Francesca Scarabel
- Department of Mathematics, University of Manchester, UK; Joint UNIversities Pandemic and Epidemiological Research, UK; CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Italy
| | - Ben Swallow
- Scottish COVID-19 Response Consortium, UK; School of Mathematics and Statistics, University of Glasgow, UK
| | - Pieter Trapman
- Department of Mathematics, Stockholm University, Stockholm, Sweden
| | - Daniel Villela
- Program of Scientific Computing, Fundação Oswaldo Cruz, Rio de Janeiro, Brazil
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9
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Valgañón P, Soriano-Paños D, Arenas A, Gómez-Gardeñes J. Contagion-diffusion processes with recurrent mobility patterns of distinguishable agents. CHAOS (WOODBURY, N.Y.) 2022; 32:043102. [PMID: 35489866 DOI: 10.1063/5.0085532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 03/16/2022] [Indexed: 06/14/2023]
Abstract
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents to alleviate analytical difficulties. Here, we address the impact that recurrent mobility patterns, and the spatial distribution of distinguishable agents, have on the unfolding of epidemics in large urban areas. We incorporate the distinguishable nature of agents regarding both their residence and their usual destination. The proposed model allows both a fast computation of the spatiotemporal pattern of the epidemic trajectory and the analytical calculation of the epidemic threshold. This threshold is found as the spectral radius of a mixing matrix encapsulating the residential distribution and the specific commuting patterns of agents. We prove that the simplification of indistinguishable individuals overestimates the value of the epidemic threshold.
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Affiliation(s)
- P Valgañón
- Department of Condensed Matter Physics, University of Zaragoza, 50009 Zaragoza, Spain
| | - D Soriano-Paños
- Instituto Gulbenkian de Ciência (IGC), 2780-156 Oeiras, Portugal
| | - A Arenas
- Departament de Matemáticas i Enginyeria Informática, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - J Gómez-Gardeñes
- Department of Condensed Matter Physics, University of Zaragoza, 50009 Zaragoza, Spain
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10
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Ventura PC, Aleta A, Aparecido Rodrigues F, Moreno Y. Modeling the effects of social distancing on the large-scale spreading of diseases. Epidemics 2022; 38:100544. [DOI: 10.1016/j.epidem.2022.100544] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Revised: 12/21/2021] [Accepted: 02/09/2022] [Indexed: 12/12/2022] Open
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11
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Ferreira CP, Marcondes D, Melo MP, Oliva SM, Peixoto CM, Peixoto PS. A snapshot of a pandemic: The interplay between social isolation and COVID-19 dynamics in Brazil. PATTERNS (NEW YORK, N.Y.) 2021; 2:100349. [PMID: 34541563 PMCID: PMC8442254 DOI: 10.1016/j.patter.2021.100349] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Revised: 07/13/2021] [Accepted: 08/20/2021] [Indexed: 06/13/2023]
Abstract
In response to the coronavirus pandemic, governments implemented social distancing, attempting to block the virus spread within territories. While it is well accepted that social isolation plays a role in epidemic control, the precise connections between mobility data indicators and epidemic dynamics are still a challenge. In this work, we investigate the dependency between a social isolation index and epidemiological metrics for several Brazilian cities. Classic statistical methods are employed to support the findings. As a first, initially surprising, result, we illustrate how there seems to be no apparent functional relationship between social isolation data and later effects on disease incidence. However, further investigations identified two regimes of successful employment of social isolation: as a preventive measure or as a remedy, albeit remedy measures require greater social isolation and bring higher burden to health systems. Additionally, we exhibit cases of successful strategies involving lockdowns and an indicator-based mobility restriction plan.
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Affiliation(s)
- Cláudia P. Ferreira
- Institute of Biosciences, São Paulo State University (UNESP), Botucatu 18618-689, Brazil
| | - Diego Marcondes
- Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
| | - Mariana P. Melo
- Department of Basic and Environmental Sciences, Engineering School of Lorena, University of São Paulo, Lorena 12602-810, Brazil
| | - Sérgio M. Oliva
- Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
| | - Cláudia M. Peixoto
- Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
| | - Pedro S. Peixoto
- Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, Brazil
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12
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Alamo T, G Reina D, Millán Gata P, Preciado VM, Giordano G. Data-driven methods for present and future pandemics: Monitoring, modelling and managing. ANNUAL REVIEWS IN CONTROL 2021; 52:448-464. [PMID: 34220287 PMCID: PMC8238691 DOI: 10.1016/j.arcontrol.2021.05.003] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Revised: 05/24/2021] [Accepted: 05/27/2021] [Indexed: 05/29/2023]
Abstract
This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.
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Affiliation(s)
- Teodoro Alamo
- Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Escuela Superior de Ingenieros, Sevilla, Spain
| | - Daniel G Reina
- Departamento de Ingeniería Electrónica, Universidad de Sevilla, Escuela Superior de Ingenieros, Sevilla, Spain
| | - Pablo Millán Gata
- Departamento de Ingeniería, Universidad Loyola Andalucía, Seville, Spain
| | - Victor M Preciado
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA
| | - Giulia Giordano
- Department of Industrial Engineering, University of Trento, Trento, Italy
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13
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García-García D, Vigo MI, Fonfría ES, Herrador Z, Navarro M, Bordehore C. Retrospective methodology to estimate daily infections from deaths (REMEDID) in COVID-19: the Spain case study. Sci Rep 2021; 11:11274. [PMID: 34050198 PMCID: PMC8163852 DOI: 10.1038/s41598-021-90051-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 05/06/2021] [Indexed: 12/15/2022] Open
Abstract
The number of new daily infections is one of the main parameters to understand the dynamics of an epidemic. During the COVID-19 pandemic in 2020, however, such information has been underestimated. Here, we propose a retrospective methodology to estimate daily infections from daily deaths, because those are usually more accurately documented. Given the incubation period, the time from illness onset to death, and the case fatality ratio, the date of death can be estimated from the date of infection. We apply this idea conversely to estimate infections from deaths. This methodology is applied to Spain and its 19 administrative regions. Our results showed that probable daily infections during the first wave were between 35 and 42 times more than those officially documented on 14 March, when the national government decreed a national lockdown and 9 times more than those documented by the updated version of the official data. The national lockdown had a strong effect on the growth rate of virus transmission, which began to decrease immediately. Finally, the first inferred infection in Spain is about 43 days before the official data were available during the first wave. The current official data show delays of 15-30 days in the first infection relative to the inferred infections in 63% of the regions. In summary, we propose a methodology that allows reinterpretation of official daily infections, improving data accuracy in infection magnitude and dates because it assimilates valuable information from the National Seroprevalence Studies.
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Affiliation(s)
| | - María Isabel Vigo
- Department of Applied Mathematics, University of Alicante, Alicante, Spain
| | - Eva S Fonfría
- Multidisciplinary Institute for Environmental Studies "Ramon Margalef", University of Alicante, Campus San Vicente del Raspeig, 03690, Alicante, Spain
| | - Zaida Herrador
- National Centre of Epidemiology, Instituto de Salud Carlos III, Madrid, Spain
| | - Miriam Navarro
- Multidisciplinary Institute for Environmental Studies "Ramon Margalef", University of Alicante, Campus San Vicente del Raspeig, 03690, Alicante, Spain
| | - Cesar Bordehore
- Multidisciplinary Institute for Environmental Studies "Ramon Margalef", University of Alicante, Campus San Vicente del Raspeig, 03690, Alicante, Spain. .,Department of Ecology, University of Alicante, Alicante, Spain.
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14
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Ketola T, Briga M, Honkola T, Lummaa V. Town population size and structuring into villages and households drive infectious disease risks in pre-healthcare Finland. Proc Biol Sci 2021; 288:20210356. [PMID: 33878921 DOI: 10.1098/rspb.2021.0356] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Social life is often considered to cost in terms of increased parasite or pathogen risk. However, evidence for this in the wild remains equivocal, possibly because populations and social groups are often structured, which affects the local transmission and extinction of diseases. We test how the structuring of towns into villages and households influenced the risk of dying from three easily diagnosable infectious diseases-smallpox, pertussis and measles-using a novel dataset covering almost all of Finland in the pre-healthcare era (1800-1850). Consistent with previous results, the risk of dying from all three diseases increased with the local population size. However, the division of towns into a larger number of villages decreased the risk of dying from smallpox and to some extent of pertussis but it slightly increased the risk for measles. Dividing towns into a larger number of households increased the length of the epidemic for all three diseases and led to the expected slower spread of the infection. However, this could be seen only when local population sizes were small. Our results indicate that the effect of population structure on epidemics, disease or parasite risk varies between pathogens and population sizes, hence lowering the ability to generalize the consequences of epidemics in spatially structured populations, and mapping the costs of social life, via parasites and diseases.
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Affiliation(s)
- Tarmo Ketola
- Department of Biological and Environmental Science, University of Jyväskylä, PO Box 35, 40014 Jyväskylä, Finland
| | - Michael Briga
- Department of Biology, University of Turku, Turku 20014, Finland
| | - Terhi Honkola
- Department of Biology, University of Turku, Turku 20014, Finland.,Department of Anthropology and Archaeology, University of Bristol, Bristol BS8 1UU, UK
| | - Virpi Lummaa
- Department of Biology, University of Turku, Turku 20014, Finland
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15
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Di Lauro F, Kiss IZ, Miller JC. Optimal timing of one-shot interventions for epidemic control. PLoS Comput Biol 2021; 17:e1008763. [PMID: 33735171 PMCID: PMC8009413 DOI: 10.1371/journal.pcbi.1008763] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2020] [Revised: 03/30/2021] [Accepted: 02/02/2021] [Indexed: 01/08/2023] Open
Abstract
The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.
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Affiliation(s)
- Francesco Di Lauro
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton United Kingdom
| | - István Z. Kiss
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton United Kingdom
| | - Joel C. Miller
- Department of Mathematics and Statistics, School of Engineering and Mathematical Sciences, La Trobe University, Bundoora, Australia
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16
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Postnikov EB. Reproducing country-wide COVID-19 dynamics can require the usage of a set of SIR systems. PeerJ 2021; 9:e10679. [PMID: 33505808 PMCID: PMC7797172 DOI: 10.7717/peerj.10679] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2020] [Accepted: 12/09/2020] [Indexed: 11/20/2022] Open
Abstract
This work shows that simple compartmental epidemiological models may not reproduce actually reported country-wide statistics since the latter reflects the cumulative amount of infected persons, which in fact is a sum of outbreaks within different patched. It the same time, the multilogistic decomposition of such epidemiological curves reveals components, which are quite close to the solutions of the SIR model in logistic approximations characterised by different sets of parameters including time shifts. This line of reasoning is confirmed by processing data for Spain and Russia in details and, additionally, is illustrated for several other countries.
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17
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Singer BJ, Thompson RN, Bonsall MB. The effect of the definition of 'pandemic' on quantitative assessments of infectious disease outbreak risk. Sci Rep 2021; 11:2547. [PMID: 33510197 PMCID: PMC7844018 DOI: 10.1038/s41598-021-81814-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 12/29/2020] [Indexed: 02/08/2023] Open
Abstract
In the early stages of an outbreak, the term 'pandemic' can be used to communicate about infectious disease risk, particularly by those who wish to encourage a large-scale public health response. However, the term lacks a widely accepted quantitative definition. We show that, under alternate quantitative definitions of 'pandemic', an epidemiological metapopulation model produces different estimates of the probability of a pandemic. Critically, we show that using different definitions alters the projected effects of key parameters-such as inter-regional travel rates, degree of pre-existing immunity, and heterogeneity in transmission rates between regions-on the risk of a pandemic. Our analysis provides a foundation for understanding the scientific importance of precise language when discussing pandemic risk, illustrating how alternative definitions affect the conclusions of modelling studies. This serves to highlight that those working on pandemic preparedness must remain alert to the variability in the use of the term 'pandemic', and provide specific quantitative definitions when undertaking one of the types of analysis that we show to be sensitive to the pandemic definition.
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Affiliation(s)
| | - Robin N Thompson
- Christ Church, University of Oxford, Oxford, UK
- Mathematical Institute, University of Oxford, Oxford, UK
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18
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Chen S, Owolabi Y, Li A, Lo E, Robinson P, Janies D, Lee C, Dulin M. Patch dynamics modeling framework from pathogens' perspective: Unified and standardized approach for complicated epidemic systems. PLoS One 2020; 15:e0238186. [PMID: 33057348 PMCID: PMC7561140 DOI: 10.1371/journal.pone.0238186] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 08/11/2020] [Indexed: 11/25/2022] Open
Abstract
Mathematical models are powerful tools to investigate, simulate, and evaluate potential interventions for infectious diseases dynamics. Much effort has focused on the Susceptible-Infected-Recovered (SIR)-type compartment models. These models consider host populations and measure change of each compartment. In this study, we propose an alternative patch dynamic modeling framework from pathogens' perspective. Each patch, the basic module of this modeling framework, has four standard mechanisms of pathogen population size change: birth (replication), death, inflow, and outflow. This framework naturally distinguishes between-host transmission process (inflow and outflow) and within-host infection process (replication) during the entire transmission-infection cycle. We demonstrate that the SIR-type model is actually a special cross-sectional and discretized case of our patch dynamics model in pathogens' viewpoint. In addition, this patch dynamics modeling framework is also an agent-based model from hosts' perspective by incorporating individual host's specific traits. We provide an operational standard to formulate this modular-designed patch dynamics model. Model parameterization is feasible with a wide range of sources, including genomics data, surveillance data, electronic health record, and from other emerging technologies such as multiomics. We then provide two proof-of-concept case studies to tackle some of the existing challenges of SIR-type models: sexually transmitted disease and healthcare acquired infections. This patch dynamics modeling framework not only provides theoretical explanations to known phenomena, but also generates novel insights of disease dynamics from a more holistic viewpoint. It is also able to simulate and handle more complicated scenarios across biological scales such as the current COVID-19 pandemic.
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Affiliation(s)
- Shi Chen
- Department of Public Health Sciences, University of North Carolina Charlotte, Charlotte, NC, United States of America
- School of Data Science, University of North Carolina Charlotte, Charlotte, NC, United States of America
| | - Yakubu Owolabi
- Department of Public Health Sciences, University of North Carolina Charlotte, Charlotte, NC, United States of America
- Division of HIV and TB, Centers for Disease Control and Prevention, Atlanta, GA, United States of America
| | - Ang Li
- State Key Laboratory of Vegetation and Environmental Change, Chinese Academy of Sciences, Beijing, China
| | - Eugenia Lo
- Department of Biological Sciences, University of North Carolina Charlotte, Charlotte, NC, United States of America
| | - Patrick Robinson
- Department of Public Health Sciences, University of North Carolina Charlotte, Charlotte, NC, United States of America
- Academy of Population Health Innovation, University of North Carolina Charlotte, Charlotte, NC, United States of America
| | - Daniel Janies
- Department of Bioinformatics, University of North Carolina Charlotte, Charlotte, NC, United States of America
| | - Chihoon Lee
- School of Business, Stevens Institute of Technology, Hoboken, NJ, United States of America
| | - Michael Dulin
- Department of Public Health Sciences, University of North Carolina Charlotte, Charlotte, NC, United States of America
- Academy of Population Health Innovation, University of North Carolina Charlotte, Charlotte, NC, United States of America
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19
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Feng L, Zhao Q, Zhou C. Epidemic in networked population with recurrent mobility pattern. CHAOS, SOLITONS, AND FRACTALS 2020; 139:110016. [PMID: 32834588 PMCID: PMC7315165 DOI: 10.1016/j.chaos.2020.110016] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
The novel Coronavirus (COVID-19) has caused a global crisis and many governments have taken social measures, such as home quarantine and maintaining social distance. Many recent studies show that network structure and human mobility greatly influence the dynamics of epidemic spreading. In this paper, we utilize a discrete-time Markov chain approach and propose an epidemic model to describe virus propagation in the heterogeneous graph, which is used to represent individuals with intra social connections and mobility between individuals and common locations. There are two types of nodes, individuals and public places, and disease can spread by social contacts among individuals and people gathering in common areas. We give theoretical results about epidemic threshold and influence of isolation factor. Several numerical simulations are performed and experimental results further demonstrate the correctness of proposed model. Non-monotonic relationship between mobility possibility and epidemic threshold and differences between Erdös-Rényi and power-law social connections are revealed. In summary, our proposed approach and findings are helpful to analyse and prevent the epidemic spreading in networked population with recurrent mobility pattern.
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Affiliation(s)
- Liang Feng
- Center for Intelligent and Networked Systems (CFINS), Department of Automation, Tsinghua University, Beijing 100084, China
- Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing 100084, China
| | - Qianchuan Zhao
- Center for Intelligent and Networked Systems (CFINS), Department of Automation, Tsinghua University, Beijing 100084, China
- Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing 100084, China
| | - Cangqi Zhou
- School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
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20
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Feng L, Zhao Q, Zhou C. Epidemic spreading in heterogeneous networks with recurrent mobility patterns. Phys Rev E 2020; 102:022306. [PMID: 32942409 DOI: 10.1103/physreve.102.022306] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 07/17/2020] [Indexed: 11/07/2022]
Abstract
Much recent research has shown that network structure and human mobility have great influences on epidemic spreading. In this paper, we propose a discrete-time Markov chain method to model susceptible-infected-susceptible epidemic dynamics in heterogeneous networks. There are two types of locations, residences and common places, for which different infection mechanisms are adopted. We also give theoretical results about the impacts of important factors, such as mobility probability and isolation, on epidemic threshold. Numerical simulations are conducted, and experimental results support our analysis. In addition, we find that the dominations of different types of residences might reverse when mobility probability varies for some networks. In summary, the findings are helpful for policy making to prevent the spreading of epidemics.
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Affiliation(s)
- Liang Feng
- Center for Intelligent and Networked Systems (CFINS), Department of Automation and BNRist, Tsinghua University, Beijing 100084, China
| | - Qianchuan Zhao
- Center for Intelligent and Networked Systems (CFINS), Department of Automation and BNRist, Tsinghua University, Beijing 100084, China
| | - Cangqi Zhou
- School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
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21
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Overton CE, Stage HB, Ahmad S, Curran-Sebastian J, Dark P, Das R, Fearon E, Felton T, Fyles M, Gent N, Hall I, House T, Lewkowicz H, Pang X, Pellis L, Sawko R, Ustianowski A, Vekaria B, Webb L. Using statistics and mathematical modelling to understand infectious disease outbreaks: COVID-19 as an example. Infect Dis Model 2020; 5:409-441. [PMID: 32691015 PMCID: PMC7334973 DOI: 10.1016/j.idm.2020.06.008] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Revised: 06/30/2020] [Accepted: 06/30/2020] [Indexed: 01/12/2023] Open
Abstract
During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic.
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Affiliation(s)
- Christopher E Overton
- Department of Mathematics, University of Manchester, UK
- Department of Mathematical Sciences, University of Liverpool, UK
| | | | - Shazaad Ahmad
- Department of Virology, Manchester Medical Microbiology Partnership, Manchester Foundation Trust, UK
- Manchester Academic Health Sciences Centre, UK
| | | | - Paul Dark
- Division of Infection, Immunity and Respiratory Medicine, NIHR Biomedical Research Centre, University of Manchester, UK
- Critical Care Unit, Salford Royal Hospital, Northern Care Alliance NHS Group, UK
| | - Rajenki Das
- Department of Mathematics, University of Manchester, UK
| | - Elizabeth Fearon
- Department of Global Health and Development, London School of Hygiene and Tropical Medicine, UK
| | - Timothy Felton
- Division of Infection, Immunity and Respiratory Medicine, NIHR Biomedical Research Centre, University of Manchester, UK
- Intensive Care Unit, Wythenshawe Hospital, Manchester University NHS Foundation Trust, UK
| | - Martyn Fyles
- Department of Mathematics, University of Manchester, UK
- The Alan Turing Institute, UK
| | - Nick Gent
- Emergency Response Department, Public Health England, UK
| | - Ian Hall
- Department of Mathematics, University of Manchester, UK
- Emergency Response Department, Public Health England, UK
| | - Thomas House
- Department of Mathematics, University of Manchester, UK
- IBM Research, Hartree Centre, SciTech Daresbury, UK
| | - Hugo Lewkowicz
- Department of Health Sciences, University of Manchester, UK
- Department of Mathematics, University of Manchester, UK
| | - Xiaoxi Pang
- Department of Mathematics, University of Manchester, UK
| | | | - Robert Sawko
- IBM Research, Hartree Centre, SciTech Daresbury, UK
| | - Andrew Ustianowski
- Regional Infectious Diseases Unit, North Manchester General Hospital, UK
- School of Medical Sciences, University of Manchester, UK
| | - Bindu Vekaria
- Department of Mathematics, University of Manchester, UK
| | - Luke Webb
- Department of Mathematics, University of Manchester, UK
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22
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Beckett SJ, Dominguez-Mirazo M, Lee S, Andris C, Weitz JS. Spread of COVID-19 through Georgia, USA. Near-term projections and impacts of social distancing via a metapopulation model. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2020:2020.05.28.20115642. [PMID: 32511490 PMCID: PMC7273258 DOI: 10.1101/2020.05.28.20115642] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Epidemiological forecasts of COVID-19 spread at the country and/or state level have helped shape public health interventions. However, such models leave a scale-gap between the spatial resolution of actionable information (i.e. the county or city level) and that of modeled viral spread. States and nations are not spatially homogeneous and different areas may vary in disease risk and severity. For example, COVID-19 has age-stratified risk. Similarly, ICU units, PPE and other vital equipment are not equally distributed within states. Here, we implement a county-level epidemiological framework to assess and forecast COVID-19 spread through Georgia, where 1,933 people have died from COVID-19 and 44,638 cases have been documented as of May 27, 2020. We find that county-level forecasts trained on heterogeneity due to clustered events can continue to predict epidemic spread over multi-week periods, potentially serving efforts to prepare medical resources, manage supply chains, and develop targeted public health interventions. We find that the premature removal of physical (social) distancing could lead to rapid increases in cases or the emergence of sustained plateaus of elevated fatalities.
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23
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Seno H. An SIS model for the epidemic dynamics with two phases of the human day-to-day activity. J Math Biol 2020. [PMID: 32270285 DOI: 10.1007/s00285-020-01491-0/figures/13] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/21/2023]
Abstract
An SIS model is analyzed to consider the contribution of community structure to the risk of the spread of a transmissible disease. We focus on the human day-to-day activity introduced by commuting to a central place for the social activity. We assume that the community is classified into two subpopulations: commuter and non-commuter, of which the commuter has two phases of the day-to-day activity: private and social. Further we take account of the combination of contact patterns in two phases, making use of mass-action and ratio-dependent types for the infection force. We investigate the dependence of the basic reproduction number on the commuter ratio and the daily expected duration at the social phase as essential factors characterizing the community structure, and show that the dependence is significantly affected by the combination of contact patterns, and that the difference in the commuter ratio could make the risk of the spread of a transmissible disease significantly different.
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Affiliation(s)
- Hiromi Seno
- Department of Computer and Mathematical Sciences, Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, Japan.
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24
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Seno H. An SIS model for the epidemic dynamics with two phases of the human day-to-day activity. J Math Biol 2020; 80:2109-2140. [PMID: 32270285 PMCID: PMC7139907 DOI: 10.1007/s00285-020-01491-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2019] [Revised: 03/13/2020] [Indexed: 01/11/2023]
Abstract
An SIS model is analyzed to consider the contribution of community structure to the risk of the spread of a transmissible disease. We focus on the human day-to-day activity introduced by commuting to a central place for the social activity. We assume that the community is classified into two subpopulations: commuter and non-commuter, of which the commuter has two phases of the day-to-day activity: private and social. Further we take account of the combination of contact patterns in two phases, making use of mass-action and ratio-dependent types for the infection force. We investigate the dependence of the basic reproduction number on the commuter ratio and the daily expected duration at the social phase as essential factors characterizing the community structure, and show that the dependence is significantly affected by the combination of contact patterns, and that the difference in the commuter ratio could make the risk of the spread of a transmissible disease significantly different.
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Affiliation(s)
- Hiromi Seno
- Department of Computer and Mathematical Sciences, Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, Japan.
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25
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Brand SP, Munywoki P, Walumbe D, Keeling MJ, Nokes DJ. Reducing respiratory syncytial virus (RSV) hospitalization in a lower-income country by vaccinating mothers-to-be and their households. eLife 2020; 9:47003. [PMID: 32216871 PMCID: PMC7556875 DOI: 10.7554/elife.47003] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Accepted: 03/26/2020] [Indexed: 01/15/2023] Open
Abstract
Respiratory syncytial virus is the leading cause of lower respiratory tract infection among infants. RSV is a priority for vaccine development. In this study, we investigate the potential effectiveness of a two-vaccine strategy aimed at mothers-to-be, thereby boosting maternally acquired antibodies of infants, and their household cohabitants, further cocooning infants against infection. We use a dynamic RSV transmission model which captures transmission both within households and communities, adapted to the changing demographics and RSV seasonality of a low-income country. Model parameters were inferred from past RSV hospitalisations, and forecasts made over a 10-year horizon. We find that a 50% reduction in RSV hospitalisations is possible if the maternal vaccine effectiveness can achieve 75 days of additional protection for newborns combined with a 75% coverage of their birth household co-inhabitants (~7.5% population coverage).
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Affiliation(s)
- Samuel Pc Brand
- Zeeman Institute of Systems Biology and Infectious Disease Research (SBIDER), University of Warwick, Warwick, United Kingdom.,School of Life Sciences, University of Warwick, Coventry, United Kingdom
| | - Patrick Munywoki
- Epidemiology and Demography Department, KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
| | - David Walumbe
- Epidemiology and Demography Department, KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
| | - Matthew J Keeling
- Zeeman Institute of Systems Biology and Infectious Disease Research (SBIDER), University of Warwick, Warwick, United Kingdom.,School of Life Sciences, University of Warwick, Coventry, United Kingdom.,Mathematics Institute, University of Warwick, Coventry, United Kingdom
| | - David James Nokes
- Zeeman Institute of Systems Biology and Infectious Disease Research (SBIDER), University of Warwick, Warwick, United Kingdom.,School of Life Sciences, University of Warwick, Coventry, United Kingdom.,Epidemiology and Demography Department, KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
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26
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Matsuki A, Tanaka G. Intervention threshold for epidemic control in susceptible-infected-recovered metapopulation models. Phys Rev E 2020; 100:022302. [PMID: 31574659 PMCID: PMC7217496 DOI: 10.1103/physreve.100.022302] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2018] [Indexed: 12/26/2022]
Abstract
Metapopulation epidemic models describe epidemic dynamics in networks of spatially distant patches connected via pathways for migration of individuals. In the present study, we deal with a susceptible-infected-recovered (SIR) metapopulation model where the epidemic process in each patch is represented by an SIR model and the mobility of individuals is assumed to be a homogeneous diffusion. We consider two types of patches including high-risk and low-risk ones under the assumption that a local patch is changed from a high-risk one to a low-risk one by an intervention. We theoretically analyze the intervention threshold which indicates the critical fraction of low-risk patches for preventing a global epidemic outbreak. We show that an intervention targeted to high-degree patches is more effective for epidemic control than a random intervention. The theoretical results are validated by Monte Carlo simulations for synthetic and realistic scale-free patch networks. The theoretical results also reveal that the intervention threshold depends on the human mobility network and the mobility rate. Our approach is useful for exploring better local interventions aimed at containment of epidemics.
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Affiliation(s)
- Akari Matsuki
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Gouhei Tanaka
- Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.,Institute for Innovation in International Engineering Education, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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27
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Hamelin FM, Allen LJS, Bokil VA, Gross LJ, Hilker FM, Jeger MJ, Manore CA, Power AG, Rúa MA, Cunniffe NJ. Coinfections by noninteracting pathogens are not independent and require new tests of interaction. PLoS Biol 2019; 17:e3000551. [PMID: 31794547 PMCID: PMC6890165 DOI: 10.1371/journal.pbio.3000551] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 11/04/2019] [Indexed: 12/26/2022] Open
Abstract
If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. However, the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death of coinfected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of coinfected hosts is expected to be higher than multiplication would suggest. By modelling the dynamics of multiple noninteracting pathogens causing chronic infections, we develop a pair of novel tests of interaction that properly account for nonindependence between pathogens causing lifelong infection. Our tests allow us to reinterpret data from previous studies including pathogens of humans, plants, and animals. Our work demonstrates how methods to identify interactions between pathogens can be updated using simple epidemic models. If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts can be obtained by simply multiplying the individual prevalences. However, even simple epidemiological models show this to be untrue. This study develops new tests for interaction between pathogens that account for this surprising lack of statistical independence.
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Affiliation(s)
- Frédéric M. Hamelin
- IGEPP, Agrocampus Ouest, INRA, Université de Rennes 1, Université Bretagne-Loire, Rennes, France
| | - Linda J. S. Allen
- Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, United States of America
| | - Vrushali A. Bokil
- Department of Mathematics, Oregon State University, Corvallis, Oregon, United States of America
| | - Louis J. Gross
- National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, Tennessee, United States of America
| | - Frank M. Hilker
- Institute of Environmental Systems Research, School of Mathematics and Computer Science, Osnabrück University, Osnabrück, Germany
| | - Michael J. Jeger
- Centre for Environmental Policy, Imperial College London, Ascot, United Kingdom
| | - Carrie A. Manore
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America
| | - Alison G. Power
- Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, New York, United States of America
| | - Megan A. Rúa
- Department of Biological Sciences, Wright State University, Dayton, Ohio, United States of America
| | - Nik J. Cunniffe
- Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom
- * E-mail:
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28
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Meakin SR, Keeling MJ. Correlations between stochastic endemic infection in multiple interacting subpopulations. J Theor Biol 2019; 483:109991. [PMID: 31487497 DOI: 10.1016/j.jtbi.2019.109991] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Revised: 08/16/2019] [Accepted: 09/02/2019] [Indexed: 11/24/2022]
Abstract
Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.
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Affiliation(s)
- Sophie R Meakin
- EPSRC & MRC Centre for Doctoral Training in Mathematics for Real-World Systems, University of Warwick, UK.
| | - Matt J Keeling
- Zeeman Institute: SBIDER, Mathematics Institute and School of Life Sciences, University of Warwick, UK
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29
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Dansu EJ, Seno H. A model for epidemic dynamics in a community with visitor subpopulation. J Theor Biol 2019; 478:115-127. [PMID: 31228488 PMCID: PMC7094103 DOI: 10.1016/j.jtbi.2019.06.020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2019] [Revised: 06/16/2019] [Accepted: 06/19/2019] [Indexed: 11/04/2022]
Abstract
With a model consisting of SIR and SIS models, we affirm claims in previous works. We derive different basic reproduction numbers looking at varying perspectives. We discuss the biological meanings of these basic reproduction numbers. All the basic reproduction numbers coincide with respect to the critical condition. Relevant public health policies are proposed based on our findings.
With a five dimensional system of ordinary differential equations based on the SIR and SIS models, we consider the dynamics of epidemics in a community which consists of residents and short-stay visitors. Taking different viewpoints to consider public health policies to control the disease, we derive different basic reproduction numbers and clarify their common/different mathematical natures so as to understand their meanings in the dynamics of the epidemic. From our analyses, the short-stay visitor subpopulation could become significant in determining the fate of diseases in the community. Furthermore, our arguments demonstrate that it is necessary to choose one variant of basic reproduction number in order to formulate appropriate public health policies.
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Affiliation(s)
- Emmanuel J Dansu
- Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 6-3-09, Aoba-ku, Sendai 980-8579, Japan.
| | - Hiromi Seno
- Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 6-3-09, Aoba-ku, Sendai 980-8579, Japan
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Spreading Processes in Multiplex Metapopulations Containing Different Mobility Networks. PHYSICAL REVIEW. X 2018; 8:031039. [PMCID: PMC7219476 DOI: 10.1103/physrevx.8.031039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We propose a theoretical framework for the study of spreading processes in structured metapopulations, with heterogeneous agents, subjected to different recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze classical epidemic models within this framework and obtain an excellent agreement with extensive Monte Carlo simulations. This agreement allows us to derive analytical expressions of the epidemic threshold and to face the challenge of characterizing a real multiplex metapopulation, the city of Medellín in Colombia, where different recurrent mobility patterns are observed depending on the socioeconomic class of the agents. Our framework allows us to unveil the geographical location of those patches that trigger the epidemic state at the critical point. A careful exploration reveals that social mixing between classes and mobility crucially determines these critical patches and, more importantly, it can produce abrupt changes of the critical properties of the epidemic onset. The spread of disease is strongly driven by how humans move and segregate across cities, regions, and countries. Understanding how epidemics arise from the interplay of these behaviors is crucial for implementing efficient containment and prevention policies. In this work, we propose a theoretical framework for the spread of pathogens that incorporates the real patterns of mobility, demographics, and human diversity observed in urban environments. Our framework represents various populations in a community as layers in a multiplex network, where nodes correspond to geographical areas and layers account for movement patterns. With this framework, we analyze a real urban system, the city of Medellin in Colombia, considering the interplay between six socioeconomic classes displaying disparate demographic segregation and mobility habits. Our framework can identify those neighborhoods and classes that trigger epidemic outbreaks. Remarkably, we observe that small changes to both mobility and social mixing among these subpopulations can trigger abrupt changes. As a consequence, containment strategies targeting a certain neighborhood can quickly change from efficient to useless. Finally, we provide a physical interpretation of the abrupt changes of those patches driving the unfolding of epidemics based on the effective number of contacts of agents. Our framework provides a reliable, time-saving platform for analyzing the spread of pathogens among various populations, allowing researchers to identify areas critical to the unfolding of diseases. With further improvements, our formalism could be extended to accommodate more sophisticated commuting patterns and epidemic models.
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Krause AL, Kurowski L, Yawar K, Van Gorder RA. Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies. J Theor Biol 2018; 449:35-52. [PMID: 29673907 DOI: 10.1016/j.jtbi.2018.04.023] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2017] [Revised: 02/17/2018] [Accepted: 04/15/2018] [Indexed: 10/17/2022]
Abstract
While deterministic metapopulation models for the spread of epidemics between populations have been well-studied in the literature, variability in disease transmission rates and interaction rates between individual agents or populations suggests the need to consider stochastic fluctuations in model parameters in order to more fully represent realistic epidemics. In the present paper, we have extended a stochastic SIS epidemic model - which introduces stochastic perturbations in the form of white noise to the force of infection (the rate of disease transmission from classes of infected to susceptible populations) - to spatial networks, thereby obtaining a stochastic epidemic metapopulation model. We solved the stochastic model numerically and found that white noise terms do not drastically change the overall long-term dynamics of the system (for sufficiently small variance of the noise) relative to the dynamics of a corresponding deterministic system. The primary difference between the stochastic and deterministic metapopulation models is that for large time, solutions tend to quasi-stationary distributions in the stochastic setting, rather than to constant steady states in the deterministic setting. We then considered different approaches to controlling the spread of a stochastic SIS epidemic over spatial networks, comparing results for a spectrum of controls utilizing local to global information about the state of the epidemic. Variation in white noise was shown to be able to counteract the treatment rate (treated curing rate) of the epidemic, requiring greater treatment rates on the part of the control and suggesting that in real-life epidemics one should be mindful of such random variations in order for a treatment to be effective. Additionally, we point out some problems using white noise perturbations as a model, but show that a truncated noise process gives qualitatively comparable behaviors without these issues.
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Affiliation(s)
- Andrew L Krause
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Lawrence Kurowski
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Kamran Yawar
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Robert A Van Gorder
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
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Temporally Varying Relative Risks for Infectious Diseases: Implications for Infectious Disease Control. Epidemiology 2018; 28:136-144. [PMID: 27748685 DOI: 10.1097/ede.0000000000000571] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Risks for disease in some population groups relative to others (relative risks) are usually considered to be consistent over time, although they are often modified by other, nontemporal factors. For infectious diseases, in which overall incidence often varies substantially over time, the patterns of temporal changes in relative risks can inform our understanding of basic epidemiologic questions. For example, recent studies suggest that temporal changes in relative risks of infection over the course of an epidemic cycle can both be used to identify population groups that drive infectious disease outbreaks, and help elucidate differences in the effect of vaccination against infection (that is relevant to transmission control) compared with its effect against disease episodes (that reflects individual protection). Patterns of change in the age groups affected over the course of seasonal outbreaks can provide clues to the types of pathogens that could be responsible for diseases for which an infectious cause is suspected. Changing apparent efficacy of vaccines during trials may provide clues to the vaccine's mode of action and/or indicate risk heterogeneity in the trial population. Declining importance of unusual behavioral risk factors may be a signal of increased local transmission of an infection. We review these developments and the related public health implications.
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Epidemiological modelling of the 2005 French riots: a spreading wave and the role of contagion. Sci Rep 2018; 8:107. [PMID: 29311553 PMCID: PMC5758762 DOI: 10.1038/s41598-017-18093-4] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Accepted: 12/02/2017] [Indexed: 11/24/2022] Open
Abstract
As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a poor suburb of Paris, then spread in all of France, lasting about three weeks. Remarkably, although there were no displacements of rioters, the riot activity did travel. Access to daily national police data has allowed us to explore the dynamics of riot propagation. Here we show that an epidemic-like model, with just a few parameters and a single sociological variable characterizing neighbourhood deprivation, accounts quantitatively for the full spatio-temporal dynamics of the riots. This is the first time that such data-driven modelling involving contagion both within and between cities (through geographic proximity or media) at the scale of a country, and on a daily basis, is performed. Moreover, we give a precise mathematical characterization to the expression “wave of riots”, and provide a visualization of the propagation around Paris, exhibiting the wave in a way not described before. The remarkable agreement between model and data demonstrates that geographic proximity played a major role in the propagation, even though information was readily available everywhere through media. Finally, we argue that our approach gives a general framework for the modelling of the dynamics of spontaneous collective uprisings.
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Berg SS, Forester JD, Craft ME. Infectious Disease in Wild Animal Populations: Examining Transmission and Control with Mathematical Models. ADVANCES IN ENVIRONMENTAL MICROBIOLOGY 2018. [PMCID: PMC7123867 DOI: 10.1007/978-3-319-92373-4_7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The mathematical modeling of ecological interactions is an essential tool in predicting the behavior of complex systems across landscapes. The scientific literature is growing with examples of models used to explore predator-prey interactions, resource selection, population growth, and dynamics of disease transmission. These models provide managers with an efficient alternative means of testing new management and control strategies without resorting to empirical testing that is often costly, time-consuming, and impractical. This chapter presents a review of four types of mathematical models used to understand and predict the spread of infectious diseases in wild animals: compartmental, metapopulation, spatial, and contact network models. Descriptions of each model’s uses and limitations are used to provide a look at the complexities involved in modeling the spread of diseases and the trade-offs that accompany selecting one modeling approach over another. Potential avenues for the improvement and use of these models in future studies are also discussed, as are specific examples of how each type of model has improved our understanding of infectious diseases in populations of wild animals.
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Mbala P, Baguelin M, Ngay I, Rosello A, Mulembakani P, Demiris N, Edmunds WJ, Muyembe JJ. Evaluating the frequency of asymptomatic Ebola virus infection. Philos Trans R Soc Lond B Biol Sci 2017; 372:rstb.2016.0303. [PMID: 28396474 DOI: 10.1098/rstb.2016.0303] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/22/2016] [Indexed: 11/12/2022] Open
Abstract
The potential for asymptomatic infection from Ebola viruses has long been questioned. Knowing the proportion of infections that are asymptomatic substantially changes the predictions made by mathematical models and alters the corresponding decisions based upon these models. To assess the degree of asymptomatic infection occurring during an Ebola virus disease (EVD) outbreak, we carried out a serological survey in the Djera district of the Equateur province of the Democratic Republic of the Congo affected by an Ebola outbreak in 2014. We sampled all asymptomatic residents (n = 182) of 48 households where at least one case of EVD was detected. To control for potential background seroprevalence of Ebola antibodies in the population, we also sampled 188 individuals from 92 households in an unaffected area with a similar demographic background. We tested the sera collected for anti-Ebola IgG and IgM antibodies at four different dilutions. We then developed a mixture model to estimate the likely number of asymptomatic patients who developed IgM and IgG responses to Ebola antigens in both groups. While we detected an association between medium to high titres and age, we did not detect any evidence of increased asymptomatic infection in the individuals who resided in the same household as cases.This article is part of the themed issue 'The 2013-2016 West African Ebola epidemic: data, decision-making and disease control'.
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Affiliation(s)
- Placide Mbala
- Institut National de Recherche Biomédicale, Kinshasa, Democratic Republic of Congo.,METABIOTA, Kinshasa, Democratic Republic of Congo
| | - Marc Baguelin
- Modelling and Economics Department, Public Health England, London NW9 5EQ, UK .,Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London WC1E 7HT, UK
| | - Ipos Ngay
- Institut National de Recherche Biomédicale, Kinshasa, Democratic Republic of Congo.,METABIOTA, Kinshasa, Democratic Republic of Congo
| | - Alicia Rosello
- Modelling and Economics Department, Public Health England, London NW9 5EQ, UK.,Institute of Health Informatics, University College London, London WC1E 6BT, UK
| | | | - Nikolaos Demiris
- Department of Statistics, Athens University of Economics and Business, Athens 10434, Greece
| | - W John Edmunds
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London WC1E 7HT, UK
| | - Jean-Jacques Muyembe
- Institut National de Recherche Biomédicale, Kinshasa, Democratic Republic of Congo
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Britton T, Ouédraogo D. SEIRS epidemics with disease fatalities in growing populations. Math Biosci 2017; 296:45-59. [PMID: 29155133 DOI: 10.1016/j.mbs.2017.11.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2017] [Revised: 09/14/2017] [Accepted: 11/14/2017] [Indexed: 10/18/2022]
Abstract
An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major outbreaks is deterministic. Depending on the values of the parameters, the following scenarios are possible. i) The disease dies out quickly, only infecting few; ii) the epidemic takes off, the number of infected individuals grows exponentially, but the fraction of infected individuals remains negligible; iii) the epidemic takes off, the number of infected grows initially quicker than the population, the disease fatalities diminish the growth rate of the population, but it remains super critical, and the fraction of infected go to an endemic equilibrium; iv) the epidemic takes off, the number of infected individuals grows initially quicker than the population, the diseases fatalities turn the exponential growth of the population to an exponential decay.
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Affiliation(s)
- Tom Britton
- Department of Mathematics, Stockholm University, Stockholm SE-106 91, Sweden.
| | - Désiré Ouédraogo
- Laboratoire de Mathématiques et Informatique (LAMI), EDST, Université Ouaga I Pr. Joseph Ki-Zerbo03 B.P.7021 Ouagadougou 03, Burkina Faso.
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37
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White LA, Forester JD, Craft ME. Dynamic, spatial models of parasite transmission in wildlife: Their structure, applications and remaining challenges. J Anim Ecol 2017; 87:559-580. [PMID: 28944450 DOI: 10.1111/1365-2656.12761] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2017] [Accepted: 09/07/2017] [Indexed: 01/26/2023]
Abstract
Individual differences in contact rate can arise from host, group and landscape heterogeneity and can result in different patterns of spatial spread for diseases in wildlife populations with concomitant implications for disease control in wildlife of conservation concern, livestock and humans. While dynamic disease models can provide a better understanding of the drivers of spatial spread, the effects of landscape heterogeneity have only been modelled in a few well-studied wildlife systems such as rabies and bovine tuberculosis. Such spatial models tend to be either purely theoretical with intrinsic limiting assumptions or individual-based models that are often highly species- and system-specific, limiting the breadth of their utility. Our goal was to review studies that have utilized dynamic, spatial models to answer questions about pathogen transmission in wildlife and identify key gaps in the literature. We begin by providing an overview of the main types of dynamic, spatial models (e.g., metapopulation, network, lattice, cellular automata, individual-based and continuous-space) and their relation to each other. We investigate different types of ecological questions that these models have been used to explore: pathogen invasion dynamics and range expansion, spatial heterogeneity and pathogen persistence, the implications of management and intervention strategies and the role of evolution in host-pathogen dynamics. We reviewed 168 studies that consider pathogen transmission in free-ranging wildlife and classify them by the model type employed, the focal host-pathogen system, and their overall research themes and motivation. We observed a significant focus on mammalian hosts, a few well-studied or purely theoretical pathogen systems, and a lack of studies occurring at the wildlife-public health or wildlife-livestock interfaces. Finally, we discuss challenges and future directions in the context of unprecedented human-mediated environmental change. Spatial models may provide new insights into understanding, for example, how global warming and habitat disturbance contribute to disease maintenance and emergence. Moving forward, better integration of dynamic, spatial disease models with approaches from movement ecology, landscape genetics/genomics and ecoimmunology may provide new avenues for investigation and aid in the control of zoonotic and emerging infectious diseases.
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Affiliation(s)
- Lauren A White
- Department of Ecology, Evolution & Behavior, University of Minnesota, St. Paul, MN, USA
| | - James D Forester
- Department of Fisheries, Wildlife, and Conservation Biology, University of Minnesota, St. Paul, MN, USA
| | - Meggan E Craft
- Department of Veterinary Population Medicine, University of Minnesota, St. Paul, MN, USA
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38
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Ball F, Britton T, Trapman P. An epidemic in a dynamic population with importation of infectives. ANN APPL PROBAB 2017. [DOI: 10.1214/16-aap1203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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39
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Feng Z, Hill AN, Curns AT, Glasser JW. Evaluating targeted interventions via meta-population models with multi-level mixing. Math Biosci 2016; 287:93-104. [PMID: 27671169 DOI: 10.1016/j.mbs.2016.09.013] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Revised: 09/16/2016] [Accepted: 09/19/2016] [Indexed: 11/18/2022]
Abstract
Among the several means by which heterogeneity can be modeled, Levins' (1969) meta-population approach preserves the most analytical tractability, a virtue to the extent that generality is desirable. When model populations are stratified, contacts among their respective sub-populations must be described. Using a simple meta-population model, Feng et al. (2015) showed that mixing among sub-populations, as well as heterogeneity in characteristics affecting sub-population reproduction numbers, must be considered when evaluating public health interventions to prevent or control infectious disease outbreaks. They employed the convex combination of preferential within- and proportional among-group contacts first described by Nold (1980) and subsequently generalized by Jacquez et al. (1988). As the utility of meta-population modeling depends on more realistic mixing functions, the authors added preferential contacts between parents and children and among co-workers (Glasser et al., 2012). Here they further generalize this function by including preferential contacts between grandparents and grandchildren, but omit workplace contacts. They also describe a general multi-level mixing scheme, provide three two-level examples, and apply two of them. In their first application, the authors describe age- and gender-specific patterns in face-to-face conversations (Mossong et al., 2008), proxies for contacts by which respiratory pathogens might be transmitted, that are consistent with everyday experience. This suggests that meta-population models with inter-generational mixing could be employed to evaluate prolonged school-closures, a proposed pandemic mitigation measure that could expose grandparents, and other elderly surrogate caregivers for working parents, to infectious children. In their second application, the authors use a meta-population SEIR model stratified by 7 age groups and 50 states plus the District of Columbia, to compare actual with optimal vaccination during the 2009-2010 influenza pandemic in the United States. They also show that vaccination efforts could have been adjusted month-to-month during the fall of 2009 to ensure maximum impact. Such applications inspire confidence in the reliability of meta-population modeling in support of public health policymaking.
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Affiliation(s)
- Zhilan Feng
- Department of Mathematics, Purdue University, West Lafayette, IN, United States
| | - Andrew N Hill
- National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention, CDC, Atlanta, GA, United States
| | - Aaron T Curns
- National Center for Immunization and Respiratory Diseases, CDC, Atlanta, GA, United States
| | - John W Glasser
- National Center for Immunization and Respiratory Diseases, CDC, Atlanta, GA, United States .
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Chowell G, Sattenspiel L, Bansal S, Viboud C. Mathematical models to characterize early epidemic growth: A review. Phys Life Rev 2016; 18:66-97. [PMID: 27451336 PMCID: PMC5348083 DOI: 10.1016/j.plrev.2016.07.005] [Citation(s) in RCA: 175] [Impact Index Per Article: 21.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2016] [Revised: 07/01/2016] [Accepted: 07/02/2016] [Indexed: 10/21/2022]
Abstract
There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.
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Affiliation(s)
- Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, GA, USA; Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
| | - Lisa Sattenspiel
- Department of Anthropology, University of Missouri, Columbia, MO, USA
| | - Shweta Bansal
- Department of Biology, Georgetown University, Washington DC, USA; Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
| | - Cécile Viboud
- Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
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Magnitude and frequency variations of vector-borne infection outbreaks using the Ross-Macdonald model: explaining and predicting outbreaks of dengue fever. Epidemiol Infect 2016; 144:3435-3450. [PMID: 27538702 DOI: 10.1017/s0950268816001448] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
The classical Ross-Macdonald model is often utilized to model vector-borne infections; however, this model fails on several fronts. First, using measured (or estimated) parameters, which values are accepted from the literature, the model predicts a much greater number of cases than what is usually observed. Second, the model predicts a single large outbreak that is followed by decades of much smaller outbreaks, which is not consistent with what is observed. Usually towns or cities report a number of recurrences for many years, even when environmental changes cannot explain the disappearance of the infection between the peaks. In this paper, we continue to examine the pitfalls in modelling this class of infections, and explain that, if properly used, the Ross-Macdonald model works and can be used to understand the patterns of epidemics and even, to some extent, be used to make predictions. We model several outbreaks of dengue fever and show that the variable pattern of yearly recurrence (or its absence) can be understood and explained by a simple Ross-Macdonald model modified to take into account human movement across a range of neighbourhoods within a city. In addition, we analyse the effect of seasonal variations in the parameters that determine the number, longevity and biting behaviour of mosquitoes. Based on the size of the first outbreak, we show that it is possible to estimate the proportion of the remaining susceptible individuals and to predict the likelihood and magnitude of the eventual subsequent outbreaks. This approach is described based on actual dengue outbreaks with different recurrence patterns from some Brazilian regions.
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42
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Vazquez-Prokopec GM, Perkins TA, Waller LA, Lloyd AL, Reiner RC, Scott TW, Kitron U. Coupled Heterogeneities and Their Impact on Parasite Transmission and Control. Trends Parasitol 2016; 32:356-367. [PMID: 26850821 PMCID: PMC4851872 DOI: 10.1016/j.pt.2016.01.001] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2015] [Revised: 12/19/2015] [Accepted: 01/05/2016] [Indexed: 12/17/2022]
Abstract
Most host-parasite systems exhibit remarkable heterogeneity in the contribution to transmission of certain individuals, locations, host infectious states, or parasite strains. While significant advancements have been made in the understanding of the impact of transmission heterogeneity in epidemic dynamics and parasite persistence and evolution, the knowledge base of the factors contributing to transmission heterogeneity is limited. We argue that research efforts should move beyond considering the impact of single sources of heterogeneity and account for complex couplings between conditions with potential synergistic impacts on parasite transmission. Using theoretical approaches and empirical evidence from various host-parasite systems, we investigate the ecological and epidemiological significance of couplings between heterogeneities and discuss their potential role in transmission dynamics and the impact of control.
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Affiliation(s)
- Gonzalo M Vazquez-Prokopec
- Department of Environmental Sciences, Emory University, Atlanta, GA, USA; Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
| | - T Alex Perkins
- Fogarty International Center, National Institutes of Health, Bethesda, MD, USA; Department of Biological Sciences and Eck Institute for Global Health, University of Notre Dame, Notre Dame, IN, USA
| | - Lance A Waller
- Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University, Atlanta, GA, USA
| | - Alun L Lloyd
- Fogarty International Center, National Institutes of Health, Bethesda, MD, USA; Biomathematics Graduate Program and Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Robert C Reiner
- Fogarty International Center, National Institutes of Health, Bethesda, MD, USA; Department of Epidemiology and Biostatistics, Indiana University, Bloomington, IN, USA
| | - Thomas W Scott
- Fogarty International Center, National Institutes of Health, Bethesda, MD, USA; Department of Entomology and Nematology, University of California Davis, Davis, CA, USA
| | - Uriel Kitron
- Department of Environmental Sciences, Emory University, Atlanta, GA, USA; Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
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43
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Chowell G, Hyman JM. A Model for Coupled Outbreaks Contained by Behavior Change. MATHEMATICAL AND STATISTICAL MODELING FOR EMERGING AND RE-EMERGING INFECTIOUS DISEASES 2016. [PMCID: PMC7123051 DOI: 10.1007/978-3-319-40413-4_3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Large epidemics such as the recent Ebola crisis in West Africa occur when local efforts to contain outbreaks fail to overcome the probabilistic onward transmission to new locations. As a result, there may be large differences in total epidemic size from similar initial conditions. This work seeks to determine the extent to which the effects of behavior changes and metapopulation coupling on epidemic size can be characterized. While mathematical models have been developed to study local containment by social distancing, intervention and other behavior changes, their connection to larger-scale transmission is relatively underdeveloped. We make use of the assumption that behavior changes limit local transmission before susceptible depletion to develop a time-varying birth-death process capturing the dynamic decrease of the transmission rate associated with behavior changes. We derive an expression for the mean outbreak size of this model and show that the distribution of outbreak sizes is approximately geometric. This allows a probabilistic extension whereby infected individuals may initiate new outbreaks. From this model we characterize the overall epidemic size as a function of the behavior change rate and the probability that an infected individual starts a new outbreak. We find good agreement between the analytical results and stochastic simulations leading to novel findings including critical learning rates that demarcate large and small epidemic sizes.
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Affiliation(s)
- Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, Georgia USA
| | - James M. Hyman
- Department of Mathematics, Tulane University, New Orleans, Louisiana USA
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44
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Rolls DA, Geard NL, Warr DJ, Nathan PM, Robins GL, Pattison PE, McCaw JM, McVernon J. Social encounter profiles of greater Melbourne residents, by location--a telephone survey. BMC Infect Dis 2015; 15:494. [PMID: 26525046 PMCID: PMC4631075 DOI: 10.1186/s12879-015-1237-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2015] [Accepted: 10/20/2015] [Indexed: 12/05/2022] Open
Abstract
Background Models of infectious disease increasingly seek to incorporate heterogeneity of social interactions to more accurately characterise disease spread. We measured attributes of social encounters in two areas of Greater Melbourne, using a telephone survey. Methods A market research company conducted computer assisted telephone interviews (CATIs) of residents of the Boroondara and Hume local government areas (LGAs), which differ markedly in ethnic composition, age distribution and household socioeconomic status. Survey items included household demographic and socio-economic characteristics, locations visited during the preceding day, and social encounters involving two-way conversation or physical contact. Descriptive summary measures were reported and compared using weight adjusted Wald tests of group means. Results The overall response rate was 37.6 %, higher in Boroondara [n = 650, (46 %)] than Hume [n = 657 (32 %)]. Survey conduct through the CATI format was challenging, with implications for representativeness and data quality. Marked heterogeneity of encounter profiles was observed across age groups and locations. Household settings afforded greatest opportunity for prolonged close contact, particularly between women and children. Young and middle-aged men reported more age-assortative mixing, often with non-household members. Preliminary comparisons between LGAs suggested that mixing occurred in different settings. In addition, gender differences in mixing with household and non-household members, including strangers, were observed by area. Conclusions Survey administration by CATI was challenging, but rich data were obtained, revealing marked heterogeneity of social behaviour. Marked dissimilarities in patterns of prolonged close mixing were demonstrated by gender. In addition, preliminary observations of between-area differences in socialisation warrant further evaluation. Electronic supplementary material The online version of this article (doi:10.1186/s12879-015-1237-9) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- David A Rolls
- Melbourne School of Psychological Sciences, The University of Melbourne, Melbourne, Australia.
| | - Nicholas L Geard
- Modelling and Simulation Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia.
| | - Deborah J Warr
- McCaughey VicHealth Community Wellbeing Unit, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia.
| | - Paula M Nathan
- Modelling and Simulation Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia.
| | - Garry L Robins
- Melbourne School of Psychological Sciences, The University of Melbourne, Melbourne, Australia.
| | - Philippa E Pattison
- Melbourne School of Psychological Sciences, The University of Melbourne, Melbourne, Australia.
| | - James M McCaw
- Modelling and Simulation Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia. .,School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia. .,Modelling and Simulation Unit, Infection and Immunity Theme, Murdoch Childrens Research Institute, Parkville, Australia.
| | - Jodie McVernon
- Modelling and Simulation Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia. .,Modelling and Simulation Unit, Infection and Immunity Theme, Murdoch Childrens Research Institute, Parkville, Australia.
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45
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Feng Z, Hill AN, Smith PJ, Glasser JW. An elaboration of theory about preventing outbreaks in homogeneous populations to include heterogeneity or preferential mixing. J Theor Biol 2015; 386:177-87. [PMID: 26375548 DOI: 10.1016/j.jtbi.2015.09.006] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Revised: 09/03/2015] [Accepted: 09/04/2015] [Indexed: 11/30/2022]
Abstract
The goal of many vaccination programs is to attain the population immunity above which pathogens introduced by infectious people (e.g., travelers from endemic areas) will not cause outbreaks. Using a simple meta-population model, we demonstrate that, if sub-populations either differ in characteristics affecting their basic reproduction numbers or if their members mix preferentially, weighted average sub-population immunities cannot be compared with the proportionally-mixing homogeneous population-immunity threshold, as public health practitioners are wont to do. Then we review the effect of heterogeneity in average per capita contact rates on the basic meta-population reproduction number. To the extent that population density affects contacts, for example, rates might differ in urban and rural sub-populations. Other differences among sub-populations in characteristics affecting their basic reproduction numbers would contribute similarly. In agreement with more recent results, we show that heterogeneous preferential mixing among sub-populations increases the basic meta-population reproduction number more than homogeneous preferential mixing does. Next we refine earlier results on the effects of heterogeneity in sub-population immunities and preferential mixing on the effective meta-population reproduction number. Finally, we propose the vector of partial derivatives of this reproduction number with respect to the sub-population immunities as a fundamentally new tool for targeting vaccination efforts.
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Affiliation(s)
- Zhilan Feng
- Department of Mathematics, Purdue University, West Lafayette, IN, USA
| | - Andrew N Hill
- National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention, CDC, Atlanta, GA, USA
| | - Philip J Smith
- National Center for Immunization and Respiratory Diseases, CDC, 1600 Clifton Road, NE, Mail Stop A-34, Atlanta, GA 30333, USA
| | - John W Glasser
- National Center for Immunization and Respiratory Diseases, CDC, 1600 Clifton Road, NE, Mail Stop A-34, Atlanta, GA 30333, USA
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46
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Pan W, Sun GQ, Jin Z. How demography-driven evolving networks impact epidemic transmission between communities. J Theor Biol 2015. [PMID: 26210776 DOI: 10.1016/j.jtbi.2015.07.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
In this paper, we develop a complex network susceptible-infected-susceptible (SIS) model to investigate the impact of demographic factors on disease spreads. We carefully capture the transmission by short-time travelers, by assuming the susceptibles randomly travel to another community, stay for a daily time scale, and return. We calculate the basic reproductive number R0 and analyze the relevant stability of the equilibria (disease-free equilibrium and endemic equilibrium) of the model by applying limiting system theory and comparison principle. The results reveal that the disease-free equilibrium is globally asymptotically stable given R0<1, whereas the condition R0>1 leads to a globally asymptotically stable endemic equilibrium. Our numerical simulations show that demographic factors, such as birth, immigration, and short-time travels, play important roles in epidemic propagation from one community to another. Moreover, we quantitatively demonstrate how the distribution of individual's network degree would affect the result of disease transmission.
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Affiliation(s)
- Wei Pan
- School of Information and Communication Engineering, North University of China, Taiyuan 030051, China
| | - Gui-Quan Sun
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China.
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47
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Ball F, Shaw L. Estimating the within-household infection rate in emerging SIR epidemics among a community of households. J Math Biol 2015; 71:1705-35. [PMID: 25820343 DOI: 10.1007/s00285-015-0872-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Revised: 03/06/2015] [Indexed: 11/26/2022]
Abstract
This paper is concerned with estimation of the within-household infection rate γL for a susceptible --> infective --> recovered epidemic among a population of households, from observation of the early, exponentially growing phase of an epidemic. Specifically, it is assumed that an estimate of the exponential growth rate is available from general data on an emerging epidemic and more-detailed, household-level data are available in a sample of households. Estimates of γL obtained using the final size distribution of single-household epidemics are usually biased owing to the emerging nature of the epidemic. A new method, which accounts correctly for the emerging nature of the epidemic, is developed by exploiting the asymptotic theory of supercritical branching processes and proved to yield a strongly consistent estimator of γL as the population and sampled households both tend to infinity in an appropriate fashion. The theory is illustrated by simulations which demonstrate that the new method is feasible for finite populations and numerical studies are used to explore how changes to the parameters governing the spread of an epidemic affect the bias of estimates based on single-household final size distributions.
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Affiliation(s)
- Frank Ball
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Laurence Shaw
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
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48
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Childs LM, Abuelezam NN, Dye C, Gupta S, Murray MB, Williams BG, Buckee CO. Modelling challenges in context: lessons from malaria, HIV, and tuberculosis. Epidemics 2015; 10:102-7. [PMID: 25843394 PMCID: PMC4451070 DOI: 10.1016/j.epidem.2015.02.002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2014] [Revised: 02/09/2015] [Accepted: 02/09/2015] [Indexed: 02/08/2023] Open
Abstract
Malaria, HIV, and tuberculosis (TB) collectively account for several million deaths each year, with all three ranking among the top ten killers in low-income countries. Despite being caused by very different organisms, malaria, HIV, and TB present a suite of challenges for mathematical modellers that are particularly pronounced in these infections, but represent general problems in infectious disease modelling, and highlight many of the challenges described throughout this issue. Here, we describe some of the unifying challenges that arise in modelling malaria, HIV, and TB, including variation in dynamics within the host, diversity in the pathogen, and heterogeneity in human contact networks and behaviour. Through the lens of these three pathogens, we provide specific examples of the other challenges in this issue and discuss their implications for informing public health efforts.
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Affiliation(s)
- Lauren M Childs
- Center for Communicable Disease Dynamics, Harvard T.H. Chan School of Public Health, Boston, MA 02115, United States; Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115, United States
| | - Nadia N Abuelezam
- Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115, United States
| | - Christopher Dye
- Office of the Director General, World Health Organization, Avenue Appia, 1211 Geneva 27, Switzerland
| | - Sunetra Gupta
- Department of Zoology, University of Oxford, Oxford OX1 3PS, United Kingdom
| | - Megan B Murray
- Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115, United States; Division of Global Health Equity, Brigham & Women's Hospital, Boston, MA 02115, United States
| | - Brian G Williams
- South African Centre for Epidemiological Modelling and Analysis, Stellenbosch, South Africa; Wits Reproductive Health and HIV Institute, University of the Witwatersrand, Johannesburg, South Africa
| | - Caroline O Buckee
- Center for Communicable Disease Dynamics, Harvard T.H. Chan School of Public Health, Boston, MA 02115, United States; Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA 02115, United States.
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49
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Frost SDW, Pybus OG, Gog JR, Viboud C, Bonhoeffer S, Bedford T. Eight challenges in phylodynamic inference. Epidemics 2015; 10:88-92. [PMID: 25843391 PMCID: PMC4383806 DOI: 10.1016/j.epidem.2014.09.001] [Citation(s) in RCA: 106] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Revised: 08/30/2014] [Accepted: 09/02/2014] [Indexed: 02/06/2023] Open
Abstract
The field of phylodynamics, which attempts to enhance our understanding of infectious disease dynamics using pathogen phylogenies, has made great strides in the past decade. Basic epidemiological and evolutionary models are now well characterized with inferential frameworks in place. However, significant challenges remain in extending phylodynamic inference to more complex systems. These challenges include accounting for evolutionary complexities such as changing mutation rates, selection, reassortment, and recombination, as well as epidemiological complexities such as stochastic population dynamics, host population structure, and different patterns at the within-host and between-host scales. An additional challenge exists in making efficient inferences from an ever increasing corpus of sequence data.
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Affiliation(s)
- Simon D W Frost
- Department of Veterinary Medicine, University of Cambridge, Cambridge, UK; Institute of Public Health, University of Cambridge, Cambridge, UK.
| | | | - Julia R Gog
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
| | - Cecile Viboud
- Fogarty International Center, National Institutes of Health, Bethesda, USA
| | | | - Trevor Bedford
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, USA
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50
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Gog JR, Pellis L, Wood JLN, McLean AR, Arinaminpathy N, Lloyd-Smith JO. Seven challenges in modeling pathogen dynamics within-host and across scales. Epidemics 2014; 10:45-8. [PMID: 25843382 DOI: 10.1016/j.epidem.2014.09.009] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Revised: 09/19/2014] [Accepted: 09/21/2014] [Indexed: 01/18/2023] Open
Abstract
The population dynamics of infectious disease is a mature field in terms of theory and to some extent, application. However for microparasites, the theory and application of models of the dynamics within a single infected host is still an open field. Further, connecting across the scales--from cellular to host level, to population level--has potential to vastly improve our understanding of pathogen dynamics and evolution. Here, we highlight seven challenges in the following areas: transmission bottlenecks, heterogeneity within host, dynamic fitness landscapes within hosts, making use of next-generation sequencing data, capturing superinfection and when and how to model more than two scales.
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Affiliation(s)
- Julia R Gog
- Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, USA; Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
| | - Lorenzo Pellis
- Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James L N Wood
- Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, USA; Disease Dynamics Unit, Department of Veterinary Medicine, University of Cambridge, Cambridge CB3 0ES, United Kingdom
| | - Angela R McLean
- Department of Zoology, Oxford Martin School, University of Oxford, South Parks Road, Oxford OX1 3PS, United Kingdom
| | - Nimalan Arinaminpathy
- Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - James O Lloyd-Smith
- Fogarty International Center, National Institutes of Health, Bethesda, MD 20892, USA; Department of Ecology and Evolutionary Biology, University of California, Los Angeles, CA 90095, USA
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