Dynamical analysis of a heroin-cocaine epidemic model with nonlinear incidence and spatial heterogeneity.

In this paper, we investigated a new heroin-cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number , which was defined by applying the next-generation operator. The threshold type results shown that if , then the drug-free steady state is globally asymptotically stable. If , then heroin-cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of by analysing the local asymptotic stability and global attractivity.