Dynamics of a discretized SIR epidemic model with distributed delay and generalized saturation incidence

Abstract

In this paper, a discrete SIR epidemic model is proposed, which distributed delay, generalized saturating incidence rate and disease-induced mortality are taken into consideration. This model is constructed from the discretization by the hybrid Euler method. The conditions for global asymptotical stability of the disease-free equilibrium and the permanence of our model are obtained. Finally, a numerical study is performed to illustrate the mathematical findings.