Threshold dynamics of an SEAIR epidemic model with application to COVID-19

The Journal of Nonlinear Sciences and its Applications

article

Z. Zheng¹  Y. Yang¹ 

[1] School of Mathematics, Statistics, Shandong Normal University

关键词: COVID-19;    SEAIR;    Lyapunov function;    global stability;    pulse vaccination;    persistent theory;   

DOI  :  10.22436/jnsa.015.02.05

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

In this paper, a Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic model with application to COVID-19 is established by capturing the key features of the disease. The global dynamics of the model is analyzed by constructing appropriate Lyapunov functions utilizing the basic reproduction number \(R_0\) as an index. We obtain that when \(R_{0}1\), the endemic equilibrium is globally asymptotically stable. Furthermore, we consider the pulse vaccination for the disease and give an impulsive differential equations model. The definition of the basic reproduction number \(R_{0}\) of this system is given by utilizing the next generation operator. By the comparison theorem and persistent theory, we obtain that when \(R_{0}<1\)}, the disease-free periodic solution is globally asymptotically stable. Otherwise, the disease will persist and there will be at least one nontrivial periodic solution. Numerical simulations to verify our conclusions are given at the end of each of these theorems.

【 授权许可】

Unknown