On the global stability of SIS, SIR and SIRS epidemic models with standard incidence

In this paper, we establish the global stability conditions of classic SIS, SIR and SIRS epidemic models with constant recruitment, disease-induced death and standard incidence rate. We will make ingenious linear combination of known functions, common quadratic and Volterra-type, and of a new class of functions, we call composite-Volterra function, for obtain a suitable Lyapunov functions. In particular, for SIRS model we prove the global stability of the endemic equilibrium under a condition of parameters.

► We study the global stability conditions of classic epidemic models. ► The models incorporate disease-induced death and standard incidence rate. ► The analysis has been achieved by construction of novel Lyapunov functions. ► We give a partial answer to open problem of the global stability of SIRS model.