Stability analysis of an SEIS epidemic model with nonlinear incidence functional and immigration

Abstract

In this research, we propose an SEIS epidemic model with immigration and nonlinear incidence rates, considering the impact of infectious forces in both the latent and infected periods. The local dynamics of an endemic equilibrium is examined. Using a suitable Lyapunov functional, we established the global asymptotic stability of the endemic equilibrium. For the SEIS model without immigration, we calculate the basic reproduction number and establish the global stability of equilibria by means of Lyapunov functionals. Finally, two examples with numerical simulations are given to illustrate the validity of our results.