Abstract
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.
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