ArticleJournal of mathematical biology2019
A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale.
Article in Journal of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- Competing control scenarios in probabilistic SIR epidemics on social-contact networks.Annals of operations research · 2022Article
- An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration.Computer methods and programs in biomedicine · 2022Article
- Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19.International journal of environmental research and public health · 2021Article
- A time-modulated Hawkes process to model the spread of COVID-19 and the impact of countermeasures.Annual reviews in control · 2021Review
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Abstract
We define and study an open stochastic SIR (Susceptible-Infected-Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Population transition intensities are assumed to be density-dependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock farming region in western France (Finistère) and epidemiological parameters corresponding to an infectious epizootic disease. Then we exhibit an exponential lower bound for the extinction time and the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using results inspired by the Freidlin-Wentzell theory of large deviations from a dynamical system.
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