Global stability for a discrete SIR epidemic model with delay in the general incidence function

摘要

In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R01, the endemic equilibrium is globally asymptotically stable.