非药物干预措施对COVID-19模型的影响  

Effects of non-pharmaceutical interventions on the COVID-19 model

作　　者：白雪花 薛亚奎[1] BAI Xuehua;XUE Yakui(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《重庆理工大学学报（自然科学）》2022年第11期241-248,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金青年科学基金项目(11301491);山西省自然科学青年基金项目(2018010221040);山西“1331”工程重点创新团队项目。

摘　　要：研究了一类包含无症状和有症状感染的COVID-19模型,考虑了非药物干预措施对传染病传播的影响。运用下一代矩阵法计算出基本再生数R_(0),并讨论了地方病平衡点的存在性。利用Routh-Hurwitz判据和LaSalle不变集原理,证明了当R_(0)<1时,无病平衡点是局部渐近稳定和全局渐近稳定的;利用中心流形理论,证明了当R_(0)>1时,地方病平衡点是局部渐近稳定的。通过数值模拟,验证了在非药物干预措施的情况下感染人群显著减少的结论。In this paper,a COVID-19 model including asymptomatic and symptomatic infections is studied,and the influence of non-pharmaceutical interventions on the spread of infectious diseases is considered.The basic reproduction number R_(0) is calculated by the next-generation matrix method and the existence of endemic equilibrium is discussed.By using Routh-Hurwitz criterion and invariance principle LaSalle,it is proved that the disease-free equilibrium is locally asymptotically stable and globally asymptotically stable when R_(0)<1.Using the center manifold theory,it is proved that the endemic equilibrium is locally asymptotically stable when R_(0)>1.Finally,the numerical simulation verifies the conclusion that the infected number of individuals significantly decreases with non-pharmaceutical interventions.

关 键 词：非药物干预措施 COVID-19 数学模型 稳定性分析 

分 类 号：O175[理学—数学]