Asymptotic behavior of SIRS models in state-dependent random environments. (November 2020)

• Record Type: Journal Article
• Authors: Bao, Jianhai; Shao, Jinghai
• Is Part Of: Nonlinear analysis. Volume 38(2020)
• Publication Date: 2020-11
• Subjects: 60J60 -- 65J05 -- 60H35; Regime-switching -- Extinction -- Persistence -- State-dependence -- Stochastic comparison; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100914
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the random change of the environment. Our contributions consist of (i) giving some sufficient conditions on extinction (persistence) of the infectious individuals even though they are persistent (resp. extinct) in certain fixed environments; (ii) revealing, for the first time, the influence of random switching of incidence functions on extinction for the infectious individuals, which has not been studied before; (iii) establishing a criterion to judge extinction of the infectious individuals for a range of random/stochastic SIRS models with state-dependent switching by developing a stochastic comparison theorem for jump processes. Moreover, some examples are given to illustrate the applications of our theory.