Qualitative analysis of generalized multistage epidemic model with immigration

A model with multiple disease stages is discussed; its main feature is that it considers a general incidence rate, functions for death and immigration rates in all populations. We show via a suitable Lyapunov function that the unique endemic equilibrium is globally asymptotically stable. We conclude that, in order to obtain the existence and global stability of the equilibrium point of general models, conditions must be imposed on the functions present in the model. In addition, the model has no basic reproduction number due to the constant flow of infected people, which makes its eradication impossible; therefore, there is no equilibrium point free of infection.