Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay

Abstract

We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number , and the heroin-using is permanent when the basic reproduction number $R_0>1$.