文章基本信息

标题：On extinction of infectious diseases for multi-group SIRS models with saturated incidence rate
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作者：Qixing Han ; Zhigang Wang
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：333
DOI：10.1186/s13662-015-0628-y
语种：English
出版社：Hindawi Publishing Corporation
摘要：We generalize the deterministic and the stochastic single-group SIRS epidemic models with saturated incidence rate introduced by Lahrouz, Omari, and Kiouach to the multi-group versions. In the deterministic multi-group model, the fact is highlighted that if the threshold R 0 ≤ 1 $\mathscr{R}_(\leq1$ , then the infective condition disappears and it means the extinction of the disease. If R 0 > 1 $\mathscr{R}_(>1$ , then there exists an endemic equilibrium in a feasible region. Allowing the noise perturbation, for the stochastic version, we utilize stochastic Lyapunov functions to show the stability of the disease-free equilibrium of system. A detailed analysis is performed on almost surely exponential stability and pth moment exponential stability of the disease-free equilibrium. We also go into several numerical simulations to illustrate how exactly the theoretical results are verified. Good agreement was observed between our theoretical results and numerical simulations. A comprehensive conclusion is provided.
关键词：multi-group SIRS model ; stochastic perturbation ; saturated incidence rate ; Brownian motion