Global stability analysis for a SEI model with nonlinear incidence rate and asymptomatic infectious state

In this paper, we propose a generalized SEI epidemic model with a general nonlinear incidence rate and death rate functions. Furthermore, we consider that those who spread the disease are the infected and the exposed. Applying the direct Lyapunov method, we prove that the endemic equilibrium is globally asymptotically stable when the basic reproduction number R0 is greater than unity and the disease free equilibrium is globally asymptotically stable when R0 is lower than unity. We conclude that in order to obtain global stability and uniqueness of the equilibrium points, monoticity is necessary but not differentiability in the functions present in the model.