基于三类感染者的COVID-19SEIR模型的定性分析  

Qualitative Analysis Based on COVID-19 SEIR Models with Different Infectivity

作　　者：吴静[1] 蔺小林[1] 李建全 翟羿江 杨欢 WU Jing;LIN Xiao-lin;LI Jian-quan;ZHAI Yi-jiang;YANG Huan(School of Mathematics and Data Sciences,Shaanxi University of Science Technology,Xi'an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《数学的实践与认识》2023年第6期205-213,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11971281)。

摘　　要：基于经典的SEIR传染病模型,将感染者分为轻度、中度、重度三类,建立了感染者不同的COVID-19SEIR传播模型.得到了其模型的基本再生数,确定了模型平衡点的存在性.通过构造Lyapunov函数和利用LaSalle不变性原理证明了平衡点的全局稳定性,用数值模拟对所得理论研究结果进行了验证,并讨论了感染者不同的人群对COVID-19传播的影响.数值模拟显示了感染者不同的三类人群对其数量达到峰值的时间差.Based on the classic SEIR epidemic model,this paper divides the infected people into three categories:mild,moderate and severe,and establishes a COVID-19 transmission model based on different infectivity.The basic reproduction number of the model is ob-tained and the existence of the equilibrium point of the model is confirmed.By constructing Lyapunov function and using LaSalle invariance principle,the global stability of equilibrium point is proved.The results of theoretical study were verified by numerical simulation,and the influence of different infection groups on the spread of the disease was discussed.It was found that different infectious disease groups had different effects on the epidemic situation.Numerical simulations also showed the impact of all three groups on the peak number of infections.

关 键 词：新冠肺炎 平衡点 全局稳定性 数值模拟 

分 类 号：R181[医药卫生—流行病学] O175[医药卫生—公共卫生与预防医学]