Stochastic Approach in Epidemic Modeling Using the SEIRS

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Résumé

The study of infectious diseases represents one of the oldest and richest sectors ofbiomathematics. The transmission dynamics of these diseases are still a major problem in math-ematical epidemiology. In this work, we propose a stochastic version of a SEIRS epidemiologicalmodel for infectious diseases evolving in a random environment for the propagation of infectiousdiseases. This random model takes into account the rates of immigration and mortality in eachcompartment and the spread of these diseases follows a four-state Markovian process. We firststudy the stability of the model and then estimate the marginal parameters (means, variances andcovariates) of each disease state over time. Real measles data are applied to the model.

Mots-clés

Stochastic processes, epidemiology, Markov chain, SEIRS.