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1. Predicting re-emergence times of dengue epidemics at low reproductive numbers: DENV1 in Rio de Janeiro, 1986-1990

   Subramanian, R ; Romeo-Aznar, V ; Ionides, E ; Codeço, CT ; Pascual, M. ( June 2020 , Journal of the Royal Society interface)

   Predicting arbovirus re-emergence remains challenging in regions with limited off-season transmission and intermittent epidemics. Current mathematical models treat the depletion and replenishment of susceptible (non-immune) hosts as the principal drivers of re-emergence, based on established understanding of highly transmissible childhood diseases with frequent epidemics. We extend an analytical approach to determine the number of ‘skip’ years preceding re-emergence for diseases with continuous seasonal transmission, population growth and under-reporting. Re-emergence times are shown to be highly sensitive to small changes in low R0 (secondary cases produced from a primary infection in a fully susceptible population). We then fit a stochastic SIR (Susceptible-Infected-Recovered) model to observed case data for the emergence of dengue serotype DENV1 in Rio de Janeiro. This aggregated city-level model substantially over-estimates observed re-emergence times either in terms of skips or outbreak probability under forward simulation. The inability of susceptible depletion and replenishment to explain re-emergence under ‘well-mixed’ conditions at a city-wide scale demonstrates a key limitation of SIR aggregated models including those applied to other arboviruses. The predictive uncertainty and high skip sensitivity to epidemiological parameters suggest a need to investigate the relevant spatial scales of susceptible depletion and the scaling of microscale transmission dynamics to formulate simpler models that apply at coarse resolutions. Introduction: 

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2. 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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3. Connectivity, reproduction number, and mobility interact to determine communities’ epidemiological superspreader potential in a metapopulation network

   https://doi.org/10.1371/journal.pcbi.1008674  

   Lieberthal, Brandon ; Gardner, Allison M. ( March 2021 , PLOS Computational Biology)

   Althouse, Benjamin Muir (Ed.)

   Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number ( R ). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R . We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R , centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R , alter host movements, or both. 

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4. Mobility and infectiousness in the spatial spread of an emerging fungal pathogen

   https://doi.org/10.1111/1365-2656.13439  

   Langwig, Kate E. ; White, J. Paul ; Parise, Katy L. ; Kaarakka, Heather M. ; Redell, Jennifer A. ; DePue, John E. ; Scullon, William H. ; Foster, Jeffrey T. ; Kilpatrick, A. Marm ; Hoyt, Joseph R. ( February 2021 , Journal of Animal Ecology)

   Emerging infectious diseases can have devastating effects on host communities, causing population collapse and species extinctions. The timing of novel pathogen arrival into naïve species communities can have consequential effects that shape the trajectory of epidemics through populations. Pathogen introductions are often presumed to occur when hosts are highly mobile. However, spread patterns can be influenced by a multitude of other factors including host body condition and infectiousness.

   White‐nose syndrome (WNS) is a seasonal emerging infectious disease of bats, which is caused by the fungal pathogenPseudogymnoascus destructans. Within‐site transmission ofP. destructansprimarily occurs over winter; however, the influence of bat mobility and infectiousness on the seasonal timing of pathogen spread to new populations is unknown. We combined data on host population dynamics and pathogen transmission from 22 bat communities to investigate the timing of pathogen arrival and the consequences of varying pathogen arrival times on disease impacts.

   We found that midwinter arrival of the fungus predominated spread patterns, suggesting that bats were most likely to spreadP.destructanswhen they are highly infectious, but have reduced mobility. In communities whereP. destructanswas detected in early winter, one species suffered higher fungal burdens and experienced more severe declines than at sites where the pathogen was detected later in the winter, suggesting that the timing of pathogen introduction had consequential effects for some bat communities. We also found evidence of source–sink population dynamics over winter, suggesting some movement among sites occurs during hibernation, even though bats at northern latitudes were thought to be fairly immobile during this period. Winter emergence behaviour symptomatic of white‐nose syndrome may further exacerbate these winter bat movements to uninfected areas.

   Our results suggest that low infectiousness during host migration may have reduced the rate of expansion of this deadly pathogen, and that elevated infectiousness during winter plays a key role in seasonal transmission. Furthermore, our results highlight the importance of both accurate estimation of the timing of pathogen spread and the consequences of varying arrival times to prevent and mitigate the effects of infectious diseases.

    

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5. Epidemic modeling with heterogeneity and social diffusion

   https://doi.org/10.1007/s00285-022-01861-w  

   Berestycki, Henri ; Desjardins, Benoît ; Weitz, Joshua S. ; Oury, Jean-Marc ( April 2023 , Journal of Mathematical Biology)

   Abstract We propose and analyze a family of epidemiological models that extend the classic Susceptible-Infectious-Recovered/Removed (SIR)-like framework to account for dynamic heterogeneity in infection risk. The family of models takes the form of a system of reaction–diffusion equations given populations structured by heterogeneous susceptibility to infection. These models describe the evolution of population-level macroscopic quantities S ,  I ,  R as in the classical case coupled with a microscopic variable f , giving the distribution of individual behavior in terms of exposure to contagion in the population of susceptibles. The reaction terms represent the impact of sculpting the distribution of susceptibles by the infection process. The diffusion and drift terms that appear in a Fokker–Planck type equation represent the impact of behavior change both during and in the absence of an epidemic. We first study the mathematical foundations of this system of reaction–diffusion equations and prove a number of its properties. In particular, we show that the system will converge back to the unique equilibrium distribution after an epidemic outbreak. We then derive a simpler system by seeking self-similar solutions to the reaction–diffusion equations in the case of Gaussian profiles. Notably, these self-similar solutions lead to a system of ordinary differential equations including classic SIR-like compartments and a new feature: the average risk level in the remaining susceptible population. We show that the simplified system exhibits a rich dynamical structure during epidemics, including plateaus, shoulders, rebounds and oscillations. Finally, we offer perspectives and caveats on ways that this family of models can help interpret the non-canonical dynamics of emerging infectious diseases, including COVID-19. 

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