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

Volume 15, Issue 2, pp 136--151 http://dx.doi.org/10.22436/jnsa.015.02.05

Publication Date: December 08, 2021 Submission Date: September 26, 2021 Revision Date: October 17, 2021 Accteptance Date: November 19, 2021

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Authors

Z. Zheng - School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P. R. China. Y. Yang - School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P. R. China.

Abstract

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 disease-free equilibrium is globally asymptotically stable. While for \(R_{0}>1\), 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.

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Keywords

• COVID-19
• SEAIR
• Lyapunov function
• global stability
• pulse vaccination
• persistent theory

MSC

•  34C60
•  37C75
•  92B05

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