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1. Simulation applications to support teaching and research in epidemiological dynamics

   https://doi.org/10.1186/s12909-022-03674-3  

   Getz, Wayne M. ; Salter, Richard ; Vissat, Ludovica Luisa ( August 2022 , BMC Medical Education)

   An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP^Ⓡ(Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.

   We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that ‘burn’ through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive valueR₀, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value ofR₀>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.

   Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

    

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2. A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies

   https://doi.org/10.3934/nhm.2022009  

   Li, Xia ; Wang, Chuntian ; Li, Hao ; Bertozzi, Andrea L. ( January 2022 , Networks & Heterogeneous Media)

   Deterministic compartmental models for infectious diseases give the mean behaviour of stochastic agent-based models. These models work well for counterfactual studies in which a fully mixed large-scale population is relevant. However, with finite size populations, chance variations may lead to significant departures from the mean. In real-life applications, finite size effects arise from the variance of individual realizations of an epidemic course about its fluid limit. In this article, we consider the classical stochastic Susceptible-Infected-Recovered (SIR) model, and derive a martingale formulation consisting of a deterministic and a stochastic component. The deterministic part coincides with the classical deterministic SIR model and we provide an upper bound for the stochastic part. Through analysis of the stochastic component depending on varying population size, we provide a theoretical explanation of finite size effects. Our theory is supported by quantitative and direct numerical simulations of theoretical infinitesimal variance. Case studies of coronavirus disease 2019 (COVID-19) transmission in smaller populations illustrate that the theory provides an envelope of possible outcomes that includes the field data.

    

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3. Epidemiology of the silent polio outbreak in Rahat, Israel, based on modeling of environmental surveillance data

   https://doi.org/10.1073/pnas.1808798115  

   Brouwer, Andrew F. ; Eisenberg, Joseph N. S. ; Pomeroy, Connor D. ; Shulman, Lester M. ; Hindiyeh, Musa ; Manor, Yossi ; Grotto, Itamar ; Koopman, James S. ; Eisenberg, Marisa C. ( October 2018 , Proceedings of the National Academy of Sciences)

   Israel experienced an outbreak of wild poliovirus type 1 (WPV1) in 2013–2014, detected through environmental surveillance of the sewage system. No cases of acute flaccid paralysis were reported, and the epidemic subsided after a bivalent oral polio vaccination (bOPV) campaign. As we approach global eradication, polio will increasingly be detected only through environmental surveillance. We developed a framework to convert quantitative polymerase chain reaction (qPCR) cycle threshold data into scaled WPV1 and OPV1 concentrations for inference within a deterministic, compartmental infectious disease transmission model. We used this approach to estimate the epidemic curve and transmission dynamics, as well as assess alternate vaccination scenarios. Our analysis estimates the outbreak peaked in late June, much earlier than previous estimates derived from analysis of stool samples, although the exact epidemic trajectory remains uncertain. We estimate the basic reproduction number was 1.62 (95% CI 1.04–2.02). Model estimates indicate that 59% (95% CI 9–77%) of susceptible individuals (primarily children under 10 years old) were infected with WPV1 over a little more than six months, mostly before the vaccination campaign onset, and that the vaccination campaign averted 10% (95% CI 1–24%) of WPV1 infections. As we approach global polio eradication, environmental monitoring with qPCR can be used as a highly sensitive method to enhance disease surveillance. Our analytic approach brings public health relevance to environmental data that, if systematically collected, can guide eradication efforts.

    

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4. STAN: spatio-temporal attention network for pandemic prediction using real-world evidence

   https://doi.org/10.1093/jamia/ocaa322  

   Gao, Junyi ; Sharma, Rakshith ; Qian, Cheng ; Glass, Lucas M. ; Spaeder, Jeffrey ; Romberg, Justin ; Sun, Jimeng ; Xiao, Cao ( January 2021 , Journal of the American Medical Informatics Association)

   We aim to develop a hybrid model for earlier and more accurate predictions for the number of infected cases in pandemics by (1) using patients’ claims data from different counties and states that capture local disease status and medical resource utilization; (2) utilizing demographic similarity and geographical proximity between locations; and (3) integrating pandemic transmission dynamics into a deep learning model.

   We proposed a spatio-temporal attention network (STAN) for pandemic prediction. It uses a graph attention network to capture spatio-temporal trends of disease dynamics and to predict the number of cases for a fixed number of days into the future. We also designed a dynamics-based loss term for enhancing long-term predictions. STAN was tested using both real-world patient claims data and COVID-19 statistics over time across US counties.

   STAN outperforms traditional epidemiological models such as susceptible-infectious-recovered (SIR), susceptible-exposed-infectious-recovered (SEIR), and deep learning models on both long-term and short-term predictions, achieving up to 87% reduction in mean squared error compared to the best baseline prediction model.

   By combining information from real-world claims data and disease case counts data, STAN can better predict disease status and medical resource utilization.

    

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5. Modelling management strategies for chronic disease in wildlife: Predictions for the control of respiratory disease in bighorn sheep

   https://doi.org/10.1111/1365-2664.14084  

   Almberg, Emily S. ; Manlove, Kezia R. ; Cassirer, E. Frances ; Ramsey, Jennifer ; Carson, Keri ; Gude, Justin ; Plowright, Raina K. ( December 2021 , Journal of Applied Ecology)

   Controlling persistent infectious disease in wildlife populations is an ongoing challenge for wildlife managers and conservationists worldwide, and chronic diseases in particular remain a pernicious problem.

   Here, we develop a dynamic pathogen transmission model capturing key features ofMycoplasma ovipneumoniaeinfection, a major cause of population declines in North American bighorn sheepOvis canadensis. We explore the effects of model assumptions and parameter values on disease dynamics, including density‐ versus frequency‐dependent transmission, the inclusion of a carrier class versus a longer infectious period, host survival rates, disease‐induced mortality and recovery rates and the epidemic growth rate. Along the way, we estimate the basic reproductive ratio,R₀, forM. ovipneumoniaein bighorn sheep to fall between approximately 1.36 and 1.74.

   We apply the model to compare efficacies across a suite of management actions following an epidemic, including test‐and‐remove, depopulation‐and‐reintroduction, range expansion, herd augmentation and density reduction.

   Our results suggest that test‐and‐remove, depopulation‐and‐reintroduction and range expansion could help persistently infected bighorn sheep herds recovery following an epidemic. By contrast, augmentation could lead to worse outcomes than those expected in the absence of management. Other management actions that improve host survival or reduce disease‐induced mortality are also likely to improve population size and persistence of chronically infected herds.

   Synthesis and applications. Dynamic transmission models like the one employed here offer a structured, logical approach for exploring hypotheses, planning field experiments and designing adaptive management. We find that management strategies that removed infected animals or isolated them within a structured metapopulation were most successful at facilitating herd recovery from a low‐prevalence, chronic pathogen. Ideally, models like ours should operate iteratively with field experiments to triangulate on better approaches for managing wildlife diseases.

    

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