具有无症状感染的新冠病毒传播模型研究

摘要：

为研究无症状感染者对新冠病毒的传播影响,建立了一个具有无症状感染的新冠病毒传播动力学模型.首先,利用下一代矩阵法求得基本再生数R0.其次,当R0<1时,应用Hurwitz判据证明了无病平衡点的局部稳定性,并通过构造Lyapunov函数的方法证明了无病平衡点的全局稳定性;当R0>1时,系统存在唯一的地方病平衡点且是局部渐近稳定的,并证明了系统的一致持续性.然后,利用最优控制理论,求得了最优控制解的表达形式.最后,通过数值模拟验证了理论结果,并对参数进行敏感性分析,说明无症状感染者对新冠病毒传播的影响程度不容忽视,应采取居家隔离措施来降低疾病的传播率.

In order to study the influence of asymptomatic infection on the transmission of novel coronavirus,a transmission dynamics model of COVID-19 with asymptomatic infection is established.First,the basic reproduction number is obtained by the next generation matrix method.Secondly,when R0<1,Hurwitz criterion is applied to prove the local stability of the disease-free equilibrium,and the global stability of the disease-free equilibrium is proved by constructing a lyapunov function;and when R0>1,there is a unique endemic equilibrium and the system is locally asymptotically stable,proving the uniform persistence of the system.Then,using the optimal control theory,the expression form of the optimal control solution is solved.Finally,the theoretical results are verified by numerical simulation,and the sensitivity analysis of the parameters showed that the influence of asymptomatic infection on the transmission of novel coronavirus can not be ignored,and compulsory isolation measures should be taken to reduce the transmission rate of the disease.

作者：

原玉茹 李淑萍

Yuan Yuru;Li Shuping(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：

中北大学数学学院

引用本文：

《betway官方app 学报（自然科学版）》 CAS 北大核心  2024年第3期71-79,共9页

Journal of Henan Normal University(Natural Science Edition)

基金：

国家自然科学基金(11701528).

关键词：

无症状感染 稳定性 一致持续 最优控制 敏感性分析

asymptomatic infection stability uniformly persistent optimal control sensitivity analysis

分类号：

O175.1 [理学—基础数学] 

具有无症状感染的新冠病毒传播模型研究.pdf