Global Behaviors for a Class of Multi-group Sirs Epidemic Models with Nonlinear Incidence Rate
نویسندگان
چکیده
Abstract. In this paper, we study a class of multi-group SIRS epidemic models with nonlinear incidence rate which have cross patch infection between different groups. The basic reproduction number R0 is calculated. By using the method of Lyapunov functions, LaSalle’s invariance principle, the theory of the nonnegative matrices and the theory of the persistence of dynamical systems, it is proved that if R0 ≤ 1 then the disease-free equilibrium is globally asymptotically stable, and if R0 > 1 then the disease in the model is uniform persistent. Furthermore, when R0 > 1, by constructing new Lyapunov functions we establish the sufficient conditions of the global asymptotic stability for the endemic equilibrium.
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