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

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 R0 as an index. We obtain that when R0 < 1, the disease-free equilibrium is globally asymptotically stable. While for R0 > 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 R0 of this system is given by utilizing the next generation operator. By the comparison theorem and persistent theory, we obtain that when R0 < 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.