Global threshold dynamics of a stochastic differential equation SIS model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:447

Article

Xu, Chuang¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

关键词: SIS epidemic model;    Global threshold dynamics;    Basic reproduction number;    Invariant density;    Stochastic differential equation;    Fokker-Planck equation;   

DOI  :  10.1016/j.jmaa.2016.10.041

来源: Elsevier

【 摘 要 】

In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in Gray et al. (2011) [8]. We present a stochastic threshold theorem in term of a stochastic basic reproduction number R-0(S): the disease dies out with probability one if R-0(S) < 1, and the disease is recurrent if R-0(S) >= 1. We prove the existence and global asymptotic stability of a unique invariant density for the Fokker-Planck equation associated with the SDE SIS model when R-0(S) > 1. In term of the profile of the invariant density, we define a persistence basic reproduction number R-0(P) and give a persistence threshold theorem: the disease dies out with large probability if R-0(P) <= 1, while persists with large probability if R-0(P) > 1. Comparing the stochastic disease prevalence with the deterministic disease prevalence, we discover that the stochastic prevalence is bigger than the deterministic prevalence if the deterministic basic reproduction number R-0(D) > 2. This shows that noise may increase severity of disease. Finally, we study the asymptotic dynamics of the stochastic SIS model as the noise vanishes and establish a sharp connection with the threshold dynamics of the deterministic SIS model in term of a Limit Stochastic Threshold Theorem. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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