Abstract
In this work, based on theory of differential systems and stability theory, we are in the first stage to study some applications of differential systems in real-world modelling problems. Here, we propose a mathematical epidemic model, namely SEIR epidemic model with saturated treatment to describe the COVID-19 infection. Based on the next–generation matrix method and the theory of Lyapunov stability, we evaluate the basic reproduction number and investigate the asymptotic behavior of disease-free equilibrium. Additionally, in the case , we also prove the existence of a unique endemic equilibrium. Finally, in order to dicuss the effect of isolation control strategies, we study the optimal control problem for this epidemic model.
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