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

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...

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Bibliographic Details
Published inPhysica A Vol. 523; pp. 677 - 690
Main Authors Caraballo, Tomás, Settati, Adel, Fatini, Mohamed El, Lahrouz, Aadil, Imlahi, Abdelouahid
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2019
Subjects
Extinction
Lévy jumps
Persistence
Positive recurrence
White noise
Persistence
Positive recurrence
White noise
Extinction
Lévy jumps
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Summary: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. •We use white noise and Lévy noise to model the dynamics of an SIS epidemic model subject to random changes produced by the external environment.•We showed that jumps encourage the extinction of the disease in the population.•Also we give a rigorous proof for the global stability of the disease-free equilibrium state, and we next establish sufficient conditions ensuring persistence of diseases.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2019.03.006