具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析  

Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate

作　　者：赵彦军 孙晓辉 苏丽 李文轩 Zhao Yanjun;Sun Xiaohui;Su Li;Li Wenxuan(International Business School,Jilin International Studies University,Changchun 130117;College of Mathematics,Jilin University,Changchun 130012)

机构地区：[1]吉林外国语大学国际商学院,长春130117 [2]吉林大学数学学院,长春130012

出　　处：《数学物理学报（A辑）》2022年第6期1861-1872,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271154)。

摘　　要：该文考虑了一类受环境噪声影响,具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型.通过构造Lyapunov函数并利用Ito公式,证明了全局正解的存在唯一性,得到了决定疾病灭绝或持久的充分条件.最后,利用Matlab进行了数值模拟来说明理论结果的正确性.In this paper,we considered a class of stochastic SIRS epidemic model with logistic growth and Beddington-DeAngelis incidence rate by white noise in the environment.By constructing Lyapunov function and applying Ito formula,the global existence and uniqueness of positive solution are proved,the sufficient conditions which determines disease extinction and permanence are obtained.Finally,matlab is used for numerical simulation to illustrate the correctness of the theoretical results.

关 键 词：SIRS传染病模型 LOGISTIC增长 Beddington-DeAngelis发生率 灭绝性 持久性 

分 类 号：O211.6[理学—概率论与数理统计]