Geodesic
Threshold dynamics of an SEAIR epidemic model with application to COVID-19
Zheng, Z.1 ; Yang, Y. 1
1 School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P. R. China
Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 2, p. 136-151.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.015.02.05
Classification : 34C60, 37C75, 92B05
Keywords: COVID-19, SEAIR, Lyapunov function, global stability, pulse vaccination, persistent theory

Zheng, Z. 1 ; Yang, Y.  1

1 School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P. R. China 
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Zheng, Z.; Yang, Y. . Threshold dynamics of an SEAIR epidemic model with application to COVID-19. Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 2, p. 136-151. doi : 10.22436/jnsa.015.02.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.02.05/

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