一类具有随机扰动的logistic SIR传染病模型的渐近行为  

The asymptotic behavior of a logistic SIR epidemic model with stochastic perturbation

作　　者：朱玲[1] ZHU Ling(School of Science, Anhui Agriculture University, Hefei 230036, China)

机构地区：[1]安徽农业大学理学院,安徽合肥230036

出　　处：《中国科学技术大学学报》2019年第11期902-911,共10页JUSTC

基　　金：the Key Projects of Youth Fund in Anhui Agricultural University(2016ZR002);the Key Project of Natural Science Research in Anhui Colleges and Universities(KJ2019A0217,KJ2017A136).

摘　　要：考虑了一类自然死亡率受环境噪声随机扰动的logistic SIR传染病模型的渐近行为.首先,论证了模型依概率1存在正解.然后通过随机Lyapunov函数方法证明了当R0<1时无病平衡点的随机稳定性,并给出了当R0>1时的一些考虑长时间状态的渐近结果.当噪声强度很小且因病死亡率满足一定条件时,模型解围绕确定性模型的解长时间随机振荡,振荡幅度随着噪声强度的减小而减小,这说明了疾病将流行.A asymptotic behavior of a stochastic logistic SIR epidemic model was studied,whose natural death rates are subject to the environmental white noise.First,it was demonstrated that the model possesses non-negative solutions with probability one.Then,the stochastically asymptotical constancy of the equilibrium was obtained by means of the stochastic Lyapunov functional technique,when R0≤1.Additionally,when R0>1,some asymptotic outcomes regarding large time behavior were given.When the noise is small and the diseased death rate is limited,the solution will oscillate around the endemic equilibrium of the deterministic model for a long time,and the fluctuation decreases with the decrease of white noise,which reflects the prevalence of the disease.

关 键 词：随机SIR模型 logistic出生率 无病平衡点 地方病平衡点 随机Lyapunov函数 随机稳定 

分 类 号：O175[理学—数学]