GLOBAL stability for SIRS epidemic models with general incidence rate and tranfer from infectious to susceptible

2017/07/20 by Cervantes-Pérez, Angel G., Avila-Vales, Eric J.
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06601

Abstract

We study a class of SIRS epidemic dynamical models with a general non-linear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, con- cave incidence rates and some non-monotonic or concave cases. We apply LaSalle's invariance principle and Lyapunov's direct method to prove that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R0 lesser or equal to 1, and the endemic equilibrium is globally asymptotically stable if R0 > 1, under some conditions imposed on the incidence function f(S; I).

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