刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:15 March 2017
年:2017
卷:447
期:2
页码:736-757
全文大小:799 K
文摘
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 : the disease dies out with probability one if , and the disease is recurrent if . 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 . In term of the profile of the invariant density, we define a persistence basic reproduction number and give a persistence threshold theorem: the disease dies out with large probability if , while persists with large probability if . 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 . 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.