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Evans A, Hart W, Longobardi S, Desikan R, Sher A, Thompson R. Reducing transmission in multiple settings is required to eliminate the risk of major Ebola outbreaks: a mathematical modelling study. J R Soc Interface 2025; 22:20240765. [PMID: 40101777 PMCID: PMC11919492 DOI: 10.1098/rsif.2024.0765] [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: 10/28/2024] [Revised: 01/15/2025] [Accepted: 02/26/2025] [Indexed: 03/20/2025] Open
Abstract
The Ebola virus (EV) persists in animal populations, with zoonotic transmission to humans occurring every few months or years. When zoonotic transmission arises, it is important to understand which interventions are most effective at preventing a major outbreak driven by human-to-human transmission. Here, we analyse a mathematical model of EV transmission and calculate the probability of a major outbreak starting from a single introduced case. We consider community, funeral and healthcare facility transmission and conduct sensitivity analyses to explore the effects of non-pharmaceutical interventions (NPIs) that influence these transmission routes. We find that, if the index case is treated in the community, then the elimination of transmission at funerals reduces the probability of a major outbreak substantially (from 0.410 to 0.066 under our baseline model parametrization). However, eliminating the risk of major outbreaks entirely requires combinations of measures that limit transmission in different settings, such as community engagement to promote safe burial practices and implementation of barrier nursing in healthcare facilities. In addition to generating insights into the drivers of Ebola outbreaks, this research provides a modelling framework for assessing the effectiveness of interventions at mitigating outbreaks of other infectious diseases with transmission in multiple settings.
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Affiliation(s)
- Abbie Evans
- Mathematical Institute, University of Oxford, Oxford, UK
| | - William Hart
- Mathematical Institute, University of Oxford, Oxford, UK
| | | | - Rajat Desikan
- Clinical Pharmacology Modelling and Simulation, Development, GSK, Stevenage, UK
| | - Anna Sher
- Clinical Pharmacology Modelling and Simulation, Development, GSK, MA, USA
| | - Robin Thompson
- Mathematical Institute, University of Oxford, Oxford, UK
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Hridoy MB, Allen LJS. Investigating seasonal disease emergence and extinction in stochastic epidemic models. Math Biosci 2025; 381:109383. [PMID: 39900333 DOI: 10.1016/j.mbs.2025.109383] [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: 08/16/2024] [Revised: 01/22/2025] [Accepted: 01/23/2025] [Indexed: 02/05/2025]
Abstract
Seasonal disease outbreaks are common in many infectious diseases such as seasonal influenza, Zika, dengue fever, Lyme disease, malaria, and cholera. Seasonal outbreaks are often due to weather patterns affecting pathogens or disease-carrying vectors or by social behavior. We investigate disease emergence and extinction in seasonal stochastic epidemic models. Specifically, we study disease emergence through seasonally varying parameters for transmission, recovery, and vector births and deaths in time-nonhomogeneous Markov chains for SIR, SEIR, and vector-host systems. A branching process approximation of the Markov chain is used to estimate the seasonal probabilities of disease extinction. Several disease outcome measures are used to compare the dynamics in seasonal and constant environments. Numerical investigations illustrate and confirm previous results derived from stochastic epidemic models. Seasonal environments often result in lower probabilities of disease emergence and smaller values of the basic reproduction number than in constant environments, and the time of peak emergence generally precedes the peak time of the seasonal driver. We identify some new results when both transmission and recovery vary seasonally. If the relative amplitude of the recovery exceeds that of transmission or if the periodicity is not synchronized in time, lower average probabilities of disease emergence occur in a constant environment than in a seasonal environment. We also investigate the timing of vector control. This investigation provides new methods and outcome measures to study seasonal infectious disease dynamics and offers new insights into the timing of prevention and control.
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Affiliation(s)
- Mahmudul Bari Hridoy
- Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States of America.
| | - Linda J S Allen
- Department of Mathematics & Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States of America
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Kaye AR, Guzzetta G, Tildesley MJ, Thompson RN. Quantifying infectious disease epidemic risks: A practical approach for seasonal pathogens. PLoS Comput Biol 2025; 21:e1012364. [PMID: 39970184 PMCID: PMC11867399 DOI: 10.1371/journal.pcbi.1012364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2024] [Revised: 02/27/2025] [Accepted: 01/23/2025] [Indexed: 02/21/2025] Open
Abstract
For many infectious diseases, the risk of outbreaks varies seasonally. If a pathogen is usually absent from a host population, a key public health policy question is whether the pathogen's arrival will initiate local transmission, which depends on the season in which arrival occurs. This question can be addressed by estimating the "probability of a major outbreak" (the probability that introduced cases will initiate sustained local transmission). A standard approach for inferring this probability exists for seasonal pathogens (involving calculating the Case Epidemic Risk; CER) based on the mathematical theory of branching processes. Under that theory, the probability of pathogen extinction is estimated, neglecting depletion of susceptible individuals. The CER is then one minus the extinction probability. However, as we show, if transmission cannot occur for long periods of the year (e.g., over winter or over summer), the pathogen will most likely go extinct, leading to a CER that is equal (or very close) to zero even if seasonal outbreaks can occur. This renders the CER uninformative in those scenarios. We therefore devise an alternative approach for inferring outbreak risks for seasonal pathogens (involving calculating the Threshold Epidemic Risk; TER). Estimation of the TER involves calculating the probability that introduced cases will initiate a local outbreak in which a threshold number of cumulative infections is exceeded before outbreak extinction. For simple seasonal epidemic models, such as the stochastic Susceptible-Infectious-Removed model, the TER can be calculated numerically (without model simulations). For more complex models, such as stochastic host-vector models, the TER can be estimated using model simulations. We demonstrate the application of our approach by considering chikungunya virus in northern Italy as a case study. In that context, transmission is most likely in summer, when environmental conditions promote vector abundance. We show that the TER provides more useful assessments of outbreak risks than the CER, enabling practically relevant risk quantification for seasonal pathogens.
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Affiliation(s)
- Alexander R Kaye
- Mathematics Institute, University of Warwick, Coventry, United Kingdom
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Coventry, United Kingdom
| | - Giorgio Guzzetta
- Centre for Health Emergencies, Bruno Kessler Foundation, Trento, Italy
| | - Michael J Tildesley
- Mathematics Institute, University of Warwick, Coventry, United Kingdom
- Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (SBIDER), University of Warwick, Coventry, United Kingdom
- School of Life Sciences, University of Warwick, Coventry, United Kingdom
| | - Robin N Thompson
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
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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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Shikongo A, Owolabi KM. On the hindering evolution of drug resistance due to intraspecific competition arising during the facilitation survival for non-genetic resistance with fractal fractional derivative order. MODELING EARTH SYSTEMS AND ENVIRONMENT 2023; 9:2637-2650. [DOI: 10.1007/s40808-022-01644-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2022] [Accepted: 12/07/2022] [Indexed: 04/01/2025]
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Southall E, Ogi-Gittins Z, Kaye AR, Hart WS, Lovell-Read FA, Thompson RN. A practical guide to mathematical methods for estimating infectious disease outbreak risks. J Theor Biol 2023; 562:111417. [PMID: 36682408 DOI: 10.1016/j.jtbi.2023.111417] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Revised: 01/13/2023] [Accepted: 01/16/2023] [Indexed: 01/21/2023]
Abstract
Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. 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)
- E Southall
- Mathematics Institute, University of Warwick, Coventry, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, UK
| | - Z Ogi-Gittins
- Mathematics Institute, University of Warwick, Coventry, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, UK
| | - A R Kaye
- Mathematics Institute, University of Warwick, Coventry, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, UK
| | - W S Hart
- Mathematical Institute, University of Oxford, Oxford, UK
| | | | - R N Thompson
- Mathematics Institute, University of Warwick, Coventry, UK; Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, Coventry, UK.
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Lovell-Read FA, Parnell S, Cunniffe NJ, Thompson RN. Using 'sentinel' plants to improve early detection of invasive plant pathogens. PLoS Comput Biol 2023; 19:e1010884. [PMID: 36730434 PMCID: PMC9928126 DOI: 10.1371/journal.pcbi.1010884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Revised: 02/14/2023] [Accepted: 01/18/2023] [Indexed: 02/04/2023] Open
Abstract
Infectious diseases of plants present an ongoing and increasing threat to international biosecurity, with wide-ranging implications. An important challenge in plant disease management is achieving early detection of invading pathogens, which requires effective surveillance through the implementation of appropriate monitoring programmes. However, when monitoring relies on visual inspection as a means of detection, surveillance is often hindered by a long incubation period (delay from infection to symptom onset) during which plants may be infectious but not displaying visible symptoms. 'Sentinel' plants-alternative susceptible host species that display visible symptoms of infection more rapidly-could be introduced to at-risk populations and included in monitoring programmes to act as early warning beacons for infection. However, while sentinel hosts exhibit faster disease progression and so allow pathogens to be detected earlier, this often comes at a cost: faster disease progression typically promotes earlier onward transmission. Here, we construct a computational model of pathogen transmission to explore this trade-off and investigate how including sentinel plants in monitoring programmes could facilitate earlier detection of invasive plant pathogens. Using Xylella fastidiosa infection in Olea europaea (European olive) as a current high profile case study, for which Catharanthus roseus (Madagascan periwinkle) is a candidate sentinel host, we apply a Bayesian optimisation algorithm to determine the optimal number of sentinel hosts to introduce for a given sampling effort, as well as the optimal division of limited surveillance resources between crop and sentinel plants. Our results demonstrate that including sentinel plants in monitoring programmes can reduce the expected prevalence of infection upon outbreak detection substantially, increasing the feasibility of local outbreak containment.
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Affiliation(s)
| | - Stephen Parnell
- Warwick Crop Centre, School of Life Sciences, University of Warwick, Coventry, United Kingdom
| | - Nik J. Cunniffe
- Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom
| | - 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
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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: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [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
| | - 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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Zheng Q, Shen J, Zhou L, Guan L. Turing pattern induced by the directed ER network and delay. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:11854-11867. [PMID: 36653978 DOI: 10.3934/mbe.2022553] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Infectious diseases generally spread along with the asymmetry of social network propagation because the asymmetry of urban development and the prevention strategies often affect the direction of the movement. But the spreading mechanism of the epidemic remains to explore in the directed network. In this paper, the main effect of the directed network and delay on the dynamic behaviors of the epidemic is investigated. The algebraic expressions of Turing instability are given to show the role of the directed network in the spread of the epidemic, which overcomes the drawback that undirected networks cannot lead to the outbreaks of infectious diseases. Then, Hopf bifurcation is analyzed to illustrate the dynamic mechanism of the periodic outbreak, which is consistent with the transmission of COVID-19. Also, the discrepancy ratio between the imported and the exported is proposed to explain the importance of quarantine policies and the spread mechanism. Finally, the theoretical results are verified by numerical simulation.
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Affiliation(s)
- Qianqian Zheng
- School of Science, Xuchang University; Henan Joint International Research Laboratory of High Performance Computation for Complex Systems, Xuchang 461000, China
| | - Jianwei Shen
- School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
| | - Lingli Zhou
- School of Mathematical Sciences, Soochow University, Suzhou 215006, China
| | - Linan Guan
- School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
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