带有隔离调整发生率的随机COVID-19模型的动力学分析  

Dynamic Analysis of a Stochastic COVID-19 Model with Quarantine-Adjusted Incidence

作　　者：王晓红 WANG Xiaohong(Department of Mathematics,Lvliang University,Lvliang 033001,Shanxi,China)

机构地区：[1]吕梁学院数学系,山西吕梁033001

出　　处：《山西师范大学学报（自然科学版）》2024年第4期23-30,共8页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：山西省高等学校教学改革创新项目(批准号:J20231358).

摘　　要：2019年12月以来,新型冠状病毒肺炎(COVID-19)传播速度非常快,感染了全球200多个国家近2亿多人.COVID-19的特点是它可以通过自由存在的病毒或空气分子迅速扩散.假设病毒的传播是随机的而不是确定的.利用连续时间马尔科夫链随机模型方法对带有随机变量的临界状态进行预测.论文考虑了一类带有隔离调整发生率的随机SIQ新型冠状病毒模型.定义了一个停时,通过构造适当的Lyapunov函数证明了停时为无穷大,从而证明了该模型唯一正解的全局存在性.通过构造紧集和适当的Lyapunov函数,证明模型解的平稳分布的存在性及其遍历性.此外还证明了疾病的灭绝性.Since December 2019,the novel coronavirus(COVID-19)spread very fast and has infected nearly 200 million people in over 200 countries.The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere.Assuming that the spread of virus follows a random process instead of deterministic.The continuous time Markov Chain through stochastic model approach has been utilized for predicting the impending states with the use of random variables.A stochastic SIQ novel coronavirus model with quarantine-adjusted incidence is considered.A stop time is defined and proved to be infinite by constructing an appropriate Lyapunov function.Thus,the global existence of the unique positive solution of the model is proved.By constructing compact set and proper Lyapunov function,the existence and ergodicity of the stationary distribution of the solution of the model are proved.In addition,the disease was proved to be exterminating.

关 键 词：新型冠状病毒肺炎 隔离调整发生率 LYAPUNOV函数 平稳分布 灭绝性 

分 类 号：O175.1[理学—数学]