Dynamical behavior of a stochastic epidemiological model: stationary distribution and extinction of a SIRS model with stochastic perturbations
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Achraf Zinihi [2] ; Moulay Rchid Sidi Ammi [2] ; Matthias Ehrhardt [1]
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[1] University of Wuppertal
University of Wuppertal
Kreisfreie Stadt Wuppertal, Alemania
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[2] AMNEA Group, Faculty of Sciences and Technics, Moulay Ismail University of Meknes
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- Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol 83, Nº. 1, 2026, págs. 23-44
- Idioma: inglés
- DOI: 10.1007/s40324-025-00381-z
- Enlaces
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Resumen
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number R0 derived from the associated deterministic model, we demonstrate the existence of a stationary distribution in the stochastic model. In addition, we study the fluctuation of the unique solution of the deterministic problem around the diseasefree equilibrium under certain conditions. In particular, we reveal scenarios where random effects induce disease extinction, contrary to the persistence predicted by the deterministic model. The theoretical insights are complemented by numerical simulations, which provide further validation of our findings.
