The asymptotic behavior of stochastically perturbed DI SIR epidemic models with saturated incidences

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• 作者：Hong Liu ^{hongliu@amss.ac.cn}  ; [Author Vitae] ; Qingshan Yang¹ ; ^{yangqs431@nenu.edu.cn}  ; [Author Vitae] ; Daqing Jiang ^{daqingj619@gmail.com}  ; [Author Vitae]
• 关键词：Ergodic property ; Exponentially stability ; Stochastic Lyapunov functions
• 刊名：Automatica
• 出版年：2012
• 期刊代码：13_00051098
• 类别：cp
• 出版时间：May, 2012
• 卷：48
• 期：5
• 页码：820-825
• 文件大小：358 K

摘要

In this paper, we consider a class of DI SIR epidemic models with saturated incidences and parameter perturbation. We investigate the asymptotic behavior according to the perturbation and the reproductive number . When the perturbation is large, the infective in every group decays exponentially to zero while the susceptible converges weakly to stationary distribution regardless of the magnitude of . When the perturbation is small, we get the same exponential stability and weak convergence if , and we use a new class of stochastic Lyapunov functions to obtain the ergodicity and positive recurrence if .