具有非线性发生率和Markov切换的随机SIRS传染病模型  

Stochastic SIRS Infectious Disease Model with Nonlinear Incidence and Markov Switching

作　　者：何雪晴 韦煜明 HE Xueqing;WEI Yuming(School of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi 541000,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541000

出　　处：《广西民族大学学报（自然科学版）》2021年第1期74-81,共8页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金(11961074)。

摘　　要：研究了一类具有非线性发生率且受环境Markov切换和白噪声扰动的随机SIRS传染病模型。首先通过构造Lyapunov函数讨论了模型正解的存在唯一性及有界性;然后根据阈值参数和Itô公式分析了疾病的灭绝性与持久性;最后通过数值模拟验证了理论结果。A class of stochastic SIRS infectious disease models with nonlinear incidence and perturbed by environmental Markov switching and white noise perturbations is studied.The existence uniqueness and boundedness of the model's positive solutionsare is first discussed by constructing a Lyapunov function;then the extinction and persistence of the diseases are analyzed according to the threshold parameters and Ito's formula;and finally the theoretical results are validated by numerical simulations.

关 键 词：传染病模型 阈值 灭绝性 持久性 Itô公式 

分 类 号：O175[理学—数学]