具有迁移效应和隔离措施的COVID-19传播模型分析  

The Analysis of COVID-19 Transmission Model with Migration Effect and Isolation Measure

作　　者：曹祯 聂麟飞[1] CAO Zhen;NIE Linfei(College of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《江西师范大学学报（自然科学版）》2021年第6期551-558,共8页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11961066);新疆维吾尔自治区自然科学基金(2021D01E12,2021D01C070)资助项目.

摘　　要：基于COVID-19传播过程中人口流动的必然性、无症状感染者的普遍性和隔离策略的有效性,该文提出了一类具有迁移效应、无症状感染者、自我防护意识和隔离策略的COVID-19传播动力学模型,利用下一代矩阵方法给出了各类子系统和全系统基本再生数的精确表达式.进一步地,通过采用线性近似理论,构造Lyapunov函数、比较原理等方法,得到了无病平衡点的全局渐近稳定性以及疾病的持久性.最后,数值模拟解释了主要的理论结果以及人口的迁移和隔离对疾病传播的影响.Based on the inevitability of population flow in the process of COVID-19 transmission,the universality of asymptomatic infection and the effectiveness of isolation strategy,the COVID-19 transmission dynamics model with migration effect,asymptomatic infection,self-protection consciousness and isolation strategy is proposed,and the next generation matrix method is used to give the exact expression of the basic production numbers of all kinds of subsystems and the whole system.Furthermore,by using the linear approximation theory,constructing Lyapunov stability theory,comparison principle,etc.,the global asymptotic stability of the disease-free equilibrium and the persistence of this disease are obtained.Finally,numerical simulations are performed to explain the main theoretical results and the impact of population migration and isolation on disease transmission.

关 键 词：COVID-19传播模型 人口迁移与自我防护 基本再生数 无病平衡点 稳定性与持久性 

分 类 号：O175[理学—数学] R181.8[理学—基础数学]