基于带有logistic增长的SEIR模型对COVID-19传播的研究  

Research on the Spread of COVID-19 Based on the SEIR Model with Logistic Growth

作　　者：翟羿江 ZHAI Yijiang(College of General Education,Shaanxi College of Communications Technology,Xi’an 710018,China)

机构地区：[1]陕西交通职业技术学院通识教育学院,陕西西安710018

出　　处：《工业微生物》2024年第5期31-34,共4页Industrial Microbiology

摘　　要：文章基于存在基础病史易感者的SEIR模型,建立了一种带有logistic增长的COVID-19传播模型,得到了其传播的基本再生数,确定了该模型平衡点的存在性;并通过构造李雅普诺夫函数,基于拉塞尔不变性原理,论证了无病平衡点的全局稳定性;还利用劳斯-赫尔维茨准则判定了地方病平衡点的局部稳定性。同时,文章探究了每次接触染病的概率系数对系统平衡点稳定性的影响,并提出系统存在极限环以及Hopf分支。数值模拟揭示了系统可能存在规律的振荡,从而进一步证实了系统存在Hopf分支。Based on the SEIR model of susceptible people with underlying diseases,a COVID-19 transmission model with logistic growth is established,the basic reproduction number of its transmission is obtained,and the existence of the equilibrium of the model is determined.Constructing the Lyapunov function and using the LaSalle invariance principle prove the global stability of the disease-free equilibrium and using the Hurwitz criterion prove the local stability of the endemic equilibrium.At the same time,the article discusses the influence of the probability coefficient of infection for each exposure on the stability of the equilibrium of the system,and provides that the system has limit cycles and Hopf bifurcation.Numerical simulations show that the system may have regular oscillations,which further confirms the existence of Hopf bifurcation.

关 键 词：COVID-19 LOGISTIC增长 基础病 平衡点 稳定性 极限环 

分 类 号：O175[理学—数学] R511[理学—基础数学]