具有饱和感染率的随机SIR传染病模型的性质分析具有饱和感染率的随机SIR传染病模型的性质分析.pdf

Advances in Applied Mathematics 应用数学进展, 2014, 3, 127-133 Published Online August 2014 in Hans. /journal/aam /10.12677/aam.2014.33019 Qualitative Analysis of a Stochastic SIR Epidemic Model with Saturated Incidence Rates 1 2 Yang Tan , Zijun Guo 1 Tongren Polytechnic College, Tongren 2 Institute of Applied Mathematics, South-China Agricultural University, Guangzhou Email: 553129685@ th th th Received: May 15 , 2014; revised: Jun. 18 , 2014; accepted: Jun. 25 , 2014 Copyright © 2014 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract A stochastically mathematical model of a stochastic SIR epidemic model with saturated incidence rates is proposed and analyzed, setting that all the death rate and incident rate are similarly per- turbed by an independent Gaussian white noise. First the paper shows that the infective population and recovered individuals will tend to zero exponentially almost surely under some additional condi- tion. In addition, a sufficient condition for the stationary distribution around the endemic infection equilibrium state of the corresponding deterministic model is derived and the solution is ergodic. Keywords Epidemic Model, Saturated Incidence Rates, Gaussian White Noise, Stationary Distribution 具有饱和感染率的随机SIR传染病模型 的性质分析 1 2 谭 杨 ，郭子君 1铜仁职业技术学院，铜仁 2华南农业大学应用数学研究所，广州 Email: 553129685@ 127 具有饱和感染率的随机SIR 传染病模型的性质分析 收稿日期：2014年5月15 日；修回日期：2014年6月18 日；录用日期：2014年6月25 日 摘 要 建立了一类具有饱和感染率的随机SIR模型，假设易感者、感染者及移出者三群体的自然死亡率和疾病感 染