具有迁移效应和隔离措施的COVID-19传播模型分析

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.

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

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.