Global stability in an SIRS model with zoonotic transmission, nonlinear incidence rate and temporary immunity

Abstract We establish and study an SIRS epidemic model for a zoonotic disease only transmitted from animals to humans but not the opposite way, with a general nonlinear incidence rate assuming that the animal population has already reached an endemic equilibrium. Due to the zoonotic transmission, there is no disease-free equilibrium and no threshold dynamics can be observed. Using a transformation of variables, we derive a Lyapunov function for the global asymptotic stability of the unique endemic equilibrium. Mathematics Subject Classification: AMS 92D30 , 34A99