Stability Analysis Of A Class Of Discrete SIRS Epidemic Model

The persistence and globally asymptotically stability of the discrete SIRS epidemic model with nonlinear incidence rates and distributed delayed Sufficient conditions for the persistence of the model are obtained by using difference inequality. When f(x,y)=βxG(y), the corresponding sufficient conditions are that G(y) is continuous and nondecreasing on [0,∞), G(y)/y is bounded and nonincreasing on (0,∞) and G(0)= 0. The conclusion of persistence in this paper extends and improves the corresponding result on [Journal of Biomathematics,2013,28(2),247-259]. If the birth rate of susceptible is equal to the death rate of susceptible, then the conclusion of this paper is discrete from of theorem 4.1 of [Appl Math Comput,2012,39,15-34]. The sufficient conditions of globally asymptotically stability for this epidemic model were also obtained by using Lyapunov functional.