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Doran JWG, Thompson RN, Yates CA, Bowness R. Mathematical methods for scaling from within-host to population-scale in infectious disease systems. Epidemics 2023; 45:100724. [PMID: 37976680 DOI: 10.1016/j.epidem.2023.100724] [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: 02/20/2023] [Revised: 06/29/2023] [Accepted: 10/26/2023] [Indexed: 11/19/2023] Open
Abstract
Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.
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Affiliation(s)
- James W G Doran
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom.
| | - Robin N Thompson
- Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, United Kingdom; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, CV4 7AL, United Kingdom; Mathematical Institute, University of Oxford, Oxford, OX2 6GG, United Kingdom
| | - Christian A Yates
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
| | - Ruth Bowness
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
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2
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Mann-Manyombe ML, Mendy A, Seydi O, Djidjou-Demasse R. Linking within- and between-host scales for understanding the evolutionary dynamics of quantitative antimicrobial resistance. J Math Biol 2023; 87:78. [PMID: 37889337 PMCID: PMC10611892 DOI: 10.1007/s00285-023-02008-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2022] [Revised: 08/30/2023] [Accepted: 09/18/2023] [Indexed: 10/28/2023]
Abstract
Understanding both the epidemiological and evolutionary dynamics of antimicrobial resistance is a major public health concern. In this paper, we propose a nested model, explicitly linking the within- and between-host scales, in which the level of resistance of the bacterial population is viewed as a continuous quantitative trait. The within-host dynamics is based on integro-differential equations structured by the resistance level, while the between-host scale is additionally structured by the time since infection. This model simultaneously captures the dynamics of the bacteria population, the evolutionary transient dynamics which lead to the emergence of resistance, and the epidemic dynamics of the host population. Moreover, we precisely analyze the model proposed by particularly performing the uniform persistence and global asymptotic results. Finally, we discuss the impact of the treatment rate of the host population in controlling both the epidemic outbreak and the average level of resistance, either if the within-host scale therapy is a success or failure. We also explore how transitions between infected populations (treated and untreated) can impact the average level of resistance, particularly in a scenario where the treatment is successful at the within-host scale.
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Affiliation(s)
- Martin L Mann-Manyombe
- MIVEGEC, Université de Montpellier, CNRS, IRD, Montpellier, France
- Département Tronc Commun, École Polytechnique de Thiès, Thies, Senegal
| | - Abdoulaye Mendy
- MIVEGEC, Université de Montpellier, CNRS, IRD, Montpellier, France
- Département Tronc Commun, École Polytechnique de Thiès, Thies, Senegal
| | - Ousmane Seydi
- Département Tronc Commun, École Polytechnique de Thiès, Thies, Senegal
| | - Ramsès Djidjou-Demasse
- MIVEGEC, Université de Montpellier, CNRS, IRD, Montpellier, France.
- Département Tronc Commun, École Polytechnique de Thiès, Thies, Senegal.
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3
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Hart WS, Park H, Jeong YD, Kim KS, Yoshimura R, Thompson RN, Iwami S. Analysis of the risk and pre-emptive control of viral outbreaks accounting for within-host dynamics: SARS-CoV-2 as a case study. Proc Natl Acad Sci U S A 2023; 120:e2305451120. [PMID: 37788317 PMCID: PMC10576149 DOI: 10.1073/pnas.2305451120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 09/07/2023] [Indexed: 10/05/2023] Open
Abstract
In the era of living with COVID-19, the risk of localised SARS-CoV-2 outbreaks remains. Here, we develop a multiscale modelling framework for estimating the local outbreak risk for a viral disease (the probability that a major outbreak results from a single case introduced into the population), accounting for within-host viral dynamics. Compared to population-level models previously used to estimate outbreak risks, our approach enables more detailed analysis of how the risk can be mitigated through pre-emptive interventions such as antigen testing. Considering SARS-CoV-2 as a case study, we quantify the within-host dynamics using data from individuals with omicron variant infections. We demonstrate that regular antigen testing reduces, but may not eliminate, the outbreak risk, depending on characteristics of local transmission. In our baseline analysis, daily antigen testing reduces the outbreak risk by 45% compared to a scenario without antigen testing. Additionally, we show that accounting for heterogeneity in within-host dynamics between individuals affects outbreak risk estimates and assessments of the impact of antigen testing. Our results therefore highlight important factors to consider when using multiscale models to design pre-emptive interventions against SARS-CoV-2 and other viruses.
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Affiliation(s)
- William S. Hart
- Mathematical Institute, University of Oxford, OxfordOX2 6GG, United Kingdom
- lnterdisciplinary Biology Laboratory, Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya464-8602, Japan
| | - Hyeongki Park
- lnterdisciplinary Biology Laboratory, Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya464-8602, Japan
| | - Yong Dam Jeong
- lnterdisciplinary Biology Laboratory, Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya464-8602, Japan
- Department of Mathematics, Pusan National University, Busan46241, South Korea
| | - Kwang Su Kim
- lnterdisciplinary Biology Laboratory, Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya464-8602, Japan
- Department of Scientific Computing, Pukyong National University, Busan48513, South Korea
| | - Raiki Yoshimura
- lnterdisciplinary Biology Laboratory, Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya464-8602, Japan
| | - Robin N. Thompson
- Mathematical Institute, University of Oxford, OxfordOX2 6GG, United Kingdom
- Mathematics Institute, University of Warwick, CoventryCV4 7AL, United Kingdom
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, CoventryCV4 7AL, United Kingdom
| | - Shingo Iwami
- lnterdisciplinary Biology Laboratory, Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya464-8602, Japan
- Institute of Mathematics for Industry, Kyushu University, Fukuoka819-0395, Japan
- Institute for the Advanced Study of Human Biology, Kyoto University, Kyoto606-8501, Japan
- Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Saitama351-0198, Japan
- NEXT-Ganken Program, Japanese Foundation for Cancer Research, Tokyo135-8550, Japan
- Science Groove Inc., Fukuoka810-0041, Japan
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4
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Giral-Barajas J, Herrera-Nolasco CI, Herrera-Valdez MA, López SI. A probabilistic approach for the study of epidemiological dynamics of infectious diseases: Basic model and properties. J Theor Biol 2023; 572:111576. [PMID: 37437710 DOI: 10.1016/j.jtbi.2023.111576] [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: 12/31/2022] [Revised: 06/23/2023] [Accepted: 07/03/2023] [Indexed: 07/14/2023]
Abstract
The dynamics of epidemiological phenomena associated to infectious diseases have long been modelled taking different approaches. However, recent pandemic events exposed many areas of opportunity to improve the existing models. We develop a stochastic model based on the idea that transitions between epidemiological stages are alike sampling processes that may involve more than one subset of the population or may be mostly dependent on time intervals defined by pathological or clinical criteria. We apply the model to simulate epidemics, analyse the final distribution of the case fatality ratio, and define a basic reproductive number to determine the existence of a probabilistic phase transition for the dynamics. The resulting modelling scheme is robust, easy to implement, and can readily lend itself for extensions aimed at answering questions that emerge from close examination of data trends, such as those emerging from the COVID-19 pandemic, and other infectious diseases.
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Affiliation(s)
- José Giral-Barajas
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
| | - Carlos Ignacio Herrera-Nolasco
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico; Laboratorio de Dinámica, Biofísica, y Fisiología de Sistemas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico
| | - Marco Arieli Herrera-Valdez
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico; Laboratorio de Dinámica, Biofísica, y Fisiología de Sistemas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico.
| | - Sergio I López
- Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico.
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5
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Whittaker DG, Herrera-Reyes AD, Hendrix M, Owen MR, Band LR, Mirams GR, Bolton KJ, Preston SP. Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models. J Theor Biol 2023; 558:111337. [PMID: 36351493 PMCID: PMC9637393 DOI: 10.1016/j.jtbi.2022.111337] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Revised: 10/16/2022] [Accepted: 10/26/2022] [Indexed: 11/08/2022]
Abstract
During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an SIR-type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".
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Affiliation(s)
- Dominic G Whittaker
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | | | - Maurice Hendrix
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK; Digital Research Service, University of Nottingham, University Park, Nottingham, NG8 1BB, UK
| | - Markus R Owen
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Leah R Band
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Gary R Mirams
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Kirsty J Bolton
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Simon P Preston
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
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6
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Thompson RN, Southall E, Daon Y, Lovell-Read FA, Iwami S, Thompson CP, Obolski U. The impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants. Front Immunol 2023; 13:1049458. [PMID: 36713397 PMCID: PMC9874934 DOI: 10.3389/fimmu.2022.1049458] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Accepted: 12/05/2022] [Indexed: 01/13/2023] Open
Abstract
Introduction A key feature of the COVID-19 pandemic has been the emergence of SARS-CoV-2 variants with different transmission characteristics. However, when a novel variant arrives in a host population, it will not necessarily lead to many cases. Instead, it may fade out, due to stochastic effects and the level of immunity in the population. Immunity against novel SARS-CoV-2 variants may be influenced by prior exposures to related viruses, such as other SARS-CoV-2 variants and seasonal coronaviruses, and the level of cross-reactive immunity conferred by those exposures. Methods Here, we investigate the impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants in a simplified scenario in which a novel SARS-CoV-2 variant is introduced after an antigenically related virus has spread in the population. We use mathematical modelling to explore the risk that the novel variant invades the population and causes a large number of cases, as opposed to fading out with few cases. Results We find that, if cross-reactive immunity is complete (i.e. someone infected by the previously circulating virus is not susceptible to the novel variant), the novel variant must be more transmissible than the previous virus to invade the population. However, in a more realistic scenario in which cross-reactive immunity is partial, we show that it is possible for novel variants to invade, even if they are less transmissible than previously circulating viruses. This is because partial cross-reactive immunity effectively increases the pool of susceptible hosts that are available to the novel variant compared to complete cross-reactive immunity. Furthermore, if previous infection with the antigenically related virus assists the establishment of infection with the novel variant, as has been proposed following some experimental studies, then even variants with very limited transmissibility are able to invade the host population. Discussion Our results highlight that fast assessment of the level of cross-reactive immunity conferred by related viruses against novel SARS-CoV-2 variants is an essential component of novel variant risk assessments.
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Affiliation(s)
- Robin N. Thompson
- Mathematics Institute, University of Warwick, Coventry, United Kingdom,Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, United Kingdom,*Correspondence: Robin N. Thompson,
| | - Emma Southall
- Mathematics Institute, University of Warwick, Coventry, United Kingdom,Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, United Kingdom
| | - Yair Daon
- 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
| | | | - Shingo Iwami
- Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Craig P. Thompson
- Division of Biomedical Sciences, Warwick Medical School, University of Warwick, Coventry, 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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7
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Generation time of the alpha and delta SARS-CoV-2 variants: an epidemiological analysis. THE LANCET INFECTIOUS DISEASES 2022; 22:603-610. [PMID: 35176230 PMCID: PMC8843191 DOI: 10.1016/s1473-3099(22)00001-9] [Citation(s) in RCA: 105] [Impact Index Per Article: 52.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 12/06/2021] [Accepted: 12/22/2021] [Indexed: 12/15/2022]
Abstract
Background In May, 2021, the delta (B.1.617.2) SARS-CoV-2 variant became dominant in the UK, superseded by the omicron (B.1.1.529) variant in December, 2021. The delta variant is associated with increased transmissibility compared with the alpha variant, which was the dominant variant in the UK between December, 2020, and May, 2021. To understand transmission and the effectiveness of interventions, we aimed to investigate whether the delta variant generation time (the interval between infections in infector–infectee pairs) is shorter—ie, transmissions are happening more quickly—than that of the alpha variant. Methods In this epidemiological analysis, we analysed transmission data from an ongoing UK Health Security Agency (UKHSA) prospective household study. Households were recruited to the study after an index case had a positive PCR test and genomic sequencing was used to determine the variant responsible. By fitting a mathematical transmission model to the data, we estimated the intrinsic generation time (which assumes a constant supply of susceptible individuals throughout infection) and the household generation time (which reflects realised transmission in the study households, accounting for susceptible depletion) for the alpha and delta variants. Findings Between February and August, 2021, 227 households consisting of 559 participants were recruited to the UKHSA study. The alpha variant was detected or assumed to be responsible for infections in 131 households (243 infections in 334 participants) recruited in February–May, and the delta variant in 96 households (174 infections in 225 participants) in May–August. The mean intrinsic generation time was shorter for the delta variant (4·7 days, 95% credible interval [CI] 4·1–5·6) than the alpha variant (5·5 days, 4·7–6·5), with 92% posterior probability. The mean household generation time was 28% (95% CI 0–48%) shorter for the delta variant (3·2 days, 95% CI 2·5–4·2) than the alpha variant (4·5 days, 3·7–5·4), with 97·5% posterior probability. Interpretation The delta variant transmits more quickly in households than the alpha variant, which can be attributed to faster depletion of susceptible individuals in households and a possible decrease in the intrinsic generation time. Interventions such as contact tracing, testing, and isolation might be less effective if transmission of the virus occurs quickly. Funding National Institute for Health Research, UK Health Security Agency, Engineering and Physical Sciences Research Council, and UK Research and Innovation.
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8
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Kretzschmar ME, Ashby B, Fearon E, Overton CE, Panovska-Griffiths J, Pellis L, Quaife M, Rozhnova G, Scarabel F, Stage HB, Swallow B, Thompson RN, Tildesley MJ, Villela D. Challenges for modelling interventions for future pandemics. Epidemics 2022; 38:100546. [PMID: 35183834 PMCID: PMC8830929 DOI: 10.1016/j.epidem.2022.100546] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 02/04/2022] [Accepted: 02/09/2022] [Indexed: 12/16/2022] Open
Abstract
Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.
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Affiliation(s)
- Mirjam E Kretzschmar
- Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht University, Utrecht, The Netherlands.
| | - Ben Ashby
- Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
| | - Elizabeth Fearon
- Department of Global Health and Development, London School of Hygiene and Tropical Medicine, London, UK; Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, UK
| | - Christopher E Overton
- Department of Mathematics, University of Manchester, UK; Joint UNIversities Pandemic and Epidemiological Research, UK; Clinical Data Science Unit, Manchester University NHS Foundation Trust, UK
| | - Jasmina Panovska-Griffiths
- The Big Data Institute, Nuffield Department of Medicine, University of Oxford, Oxford, UK; The Queen's College, University of Oxford, Oxford, UK
| | - Lorenzo Pellis
- Department of Mathematics, University of Manchester, UK; Joint UNIversities Pandemic and Epidemiological Research, UK; The Alan Turing Institute, London, UK
| | - Matthew Quaife
- TB Modelling Group, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, UK
| | - Ganna Rozhnova
- Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht University, Utrecht, The Netherlands; BioISI-Biosystems & Integrative Sciences Institute, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal
| | - 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
| | - Helena B Stage
- Department of Mathematics, University of Manchester, UK; Joint UNIversities Pandemic and Epidemiological Research, UK; University of Potsdam, Germany; Humboldt University of Berlin, Germany
| | - Ben Swallow
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK; Scottish Covid-19 Response Consortium, UK
| | - Robin N Thompson
- Joint UNIversities Pandemic and Epidemiological Research, UK; Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK
| | - Michael J Tildesley
- Joint UNIversities Pandemic and Epidemiological Research, UK; Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry CV4 7AL, UK
| | - Daniel Villela
- Program of Scientific Computing, Oswaldo Cruz Foundation, Rio de Janeiro, Brazil
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Peterson JD, Adhikari R. Efficient and flexible methods for simulating models of time since infection. Phys Rev E 2021; 104:024410. [PMID: 34525537 DOI: 10.1103/physreve.104.024410] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 07/22/2021] [Indexed: 12/23/2022]
Abstract
Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial stages or compartments (e.g., exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with compartments are more common than TSI models, largely due to the higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a compartment model with three or four stages for the infected class. We also provide a perspective for adding stages to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an Appendix. Finally, as proof of principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by nonpharmaceutical intervention. Many of the tools described in this paper are available through the software package pyross.
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Affiliation(s)
- Joseph D Peterson
- University of Cambridge, DAMTP, Center for Mathematical Sciences, Wilberforce Rd., Cambridge CB3 0WA, United Kingdom
| | - Ronojoy Adhikari
- University of Cambridge, DAMTP, Center for Mathematical Sciences, Wilberforce Rd., Cambridge CB3 0WA, United Kingdom
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10
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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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11
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Hart WS, Maini PK, Thompson RN. High infectiousness immediately before COVID-19 symptom onset highlights the importance of continued contact tracing. eLife 2021; 10:e65534. [PMID: 33899740 PMCID: PMC8195606 DOI: 10.7554/elife.65534] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 04/25/2021] [Indexed: 01/03/2023] Open
Abstract
Background Understanding changes in infectiousness during SARS-COV-2 infections is critical to assess the effectiveness of public health measures such as contact tracing. Methods Here, we develop a novel mechanistic approach to infer the infectiousness profile of SARS-COV-2-infected individuals using data from known infector-infectee pairs. We compare estimates of key epidemiological quantities generated using our mechanistic method with analogous estimates generated using previous approaches. Results The mechanistic method provides an improved fit to data from SARS-CoV-2 infector-infectee pairs compared to commonly used approaches. Our best-fitting model indicates a high proportion of presymptomatic transmissions, with many transmissions occurring shortly before the infector develops symptoms. Conclusions High infectiousness immediately prior to symptom onset highlights the importance of continued contact tracing until effective vaccines have been distributed widely, even if contacts from a short time window before symptom onset alone are traced. Funding Engineering and Physical Sciences Research Council (EPSRC).
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Affiliation(s)
- William S Hart
- Mathematical Institute, University of OxfordOxfordUnited Kingdom
| | - Philip K Maini
- Mathematical Institute, University of OxfordOxfordUnited Kingdom
| | - Robin N Thompson
- Mathematics Institute, University of WarwickCoventryUnited Kingdom
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of WarwickCoventryUnited Kingdom
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12
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Sachak-Patwa R, Byrne HM, Thompson RN. Accounting for cross-immunity can improve forecast accuracy during influenza epidemics. Epidemics 2020; 34:100432. [PMID: 33360870 DOI: 10.1016/j.epidem.2020.100432] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2020] [Revised: 12/11/2020] [Accepted: 12/15/2020] [Indexed: 11/17/2022] Open
Abstract
Previous exposure to influenza viruses confers cross-immunity against future infections with related strains. However, this is not always accounted for explicitly in mathematical models used for forecasting during influenza outbreaks. We show that, if an influenza outbreak is due to a strain that is similar to one that has emerged previously, then accounting for cross-immunity explicitly can improve the accuracy of real-time forecasts. To do this, we consider two infectious disease outbreak forecasting models. In the first (the "1-group model"), all individuals are assumed to be identical and cross-immunity is not accounted for. In the second (the "2-group model"), individuals who have previously been infected by a related strain are assumed to be less likely to experience severe disease, and therefore recover more quickly, than immunologically naive individuals. We fit both models to estimated case notification data (including symptomatic individuals as well as laboratory-confirmed cases) from Japan from the 2009 H1N1 influenza pandemic, and then generate synthetic data for a future outbreak by assuming that the 2-group model represents the epidemiology of influenza infections more accurately. We use the 1-group model (as well as the 2-group model for comparison) to generate forecasts that would be obtained in real-time as the future outbreak is ongoing, using parameter values estimated from the 2009 epidemic as informative priors, motivated by the fact that without using prior information from 2009, the forecasts are highly uncertain. In the scenario that we consider, the 1-group model only produces accurate outbreak forecasts once the peak of the epidemic has passed, even when the values of important epidemiological parameters such as the lengths of the mean incubation and infectious periods are known exactly. As a result, it is necessary to use the more epidemiologically realistic 2-group model to generate accurate forecasts. Accounting for cross-immunity driven by exposures in previous outbreaks explicitly is expected to improve the accuracy of epidemiological modelling forecasts during influenza outbreaks.
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Affiliation(s)
- Rahil Sachak-Patwa
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
| | - Helen M Byrne
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
| | - Robin N Thompson
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK; Christ Church, University of Oxford, St Aldates, Oxford, OX1 1DP, UK; Present address: Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, UK
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Thompson RN, Gilligan CA, Cunniffe NJ. Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic. J R Soc Interface 2020; 17:20200690. [PMID: 33171074 PMCID: PMC7729054 DOI: 10.1098/rsif.2020.0690] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.
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Affiliation(s)
- R N Thompson
- Mathematical Institute, University of Oxford, Oxford, UK.,Christ Church, University of Oxford, Oxford, UK
| | - C A Gilligan
- Department of Plant Sciences, University of Cambridge, Cambridge, UK
| | - N J Cunniffe
- Department of Plant Sciences, University of Cambridge, Cambridge, UK
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