Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation

Tomás Caraballo, Adel Settati, Mohamed El Fatini, Aadil Lahrouz and Abdelouahid Imlahi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 523, issue C, 677-690

Abstract: Focusing on epidemic model in random environments, this paper uses white noise and Lévy noise to model the dynamics of the SIS epidemic model subject to the random changes of the external environment. We show that the jump encourages the extinction of the disease in the population. We first, give a rigorous proof of the global stability of the disease-free equilibrium state. We also establish sufficient conditions for the persistence of the disease. The presented results are demonstrated by numerical simulations.

Keywords: White noise; Lévy jumps; Extinction; Persistence; Positive recurrence (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:523:y:2019:i:c:p:677-690

DOI: 10.1016/j.physa.2019.03.006

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