Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence

Mohamed El Fatini, Mohamed El Khalifi, Richard Gerlach, Aziz Laaribi and Regragui Taki

Physica A: Statistical Mechanics and its Applications, 2019, vol. 534, issue C

Abstract: In this paper, we consider a stochastic epidemic model with relapse, cure and a non-linear incidence rate function. Firstly, we show the existence and uniqueness of a global positive solution. Then, in terms of a stochastic threshold Rs0, we prove the extinction of the disease when Rs0<1. We also establish the persistence in mean of the epidemic in the case of Rs0>1. Furthermore, we prove the existence of a stationary distribution and its asymptotic stability. Finally, we present numerical simulations for the stochastic model to support the theoretical results.

Keywords: Epidemic model; Extinction; Persistence; Stationary distribution (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119302961

DOI: 10.1016/j.physa.2019.03.061

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