基于人口流动的COVID-19传播动力学模型研究  

Study on the Transmission Dynamics Model of COVID-19with Population Mobility

作　　者：郭文丹 聂麟飞[1] GUO Wendan;NIE Linfei(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2022年第2期161-168,共8页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金项目(11961066);新疆维吾尔自治区高校科研计划项目(XJEDU2018I001)。

摘　　要：地区之间的人口流动是当前乃至今后一段时期COVID-19传播的主要途径之一.基于病毒在人群和宿主之间的传播规律以及人口迁移的影响,提出了一类具有迁移效应,无症状感染者和隔离措施的COVID-19传播动力学模型,并利用下一代矩阵方法给出了基本再生数的精确表达式.进一步,利用线性近似和构造Lyapunov函数的方法,证明了当基本再生数小于1时,无感染平衡态是全局渐近稳定的;而当基本再生数大于1时,疾病是一致持久的.数值模拟解释了主要的理论结果并验证了防控措施的可行性.Population flow is one of the main ways of COVID-19 transmission at present and in the future.Based on the law of virus transmission between people and hosts, and the influence of population migration, a kind of COVID-19 transmission dynamic model with migration effect, asymptomatic infection and isolation measures is proposed, and the accurate expression of basic reproduction number is given by using next generation matrix method. Further, by using the method and skill of linear approximation and Lyapunov function, it is proved that when the basic reproduction number is less than 1, the disease-free equilibrium is globally asymptotically stable;when the basic reproduction number is greater than 1, the disease is uniformly persistent. Numerical simulation explains the main theoretical results and verifies the feasibility of the control measures.

关 键 词：COVID-19传播模型 人口流动 基本再生数 无感染平衡态与地方病平衡态 稳定性与持久性 

分 类 号：O175[理学—数学]