LAUSR

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 R0, which was defined by applying the next-generation operator. The threshold type results shown that if R0<1, then the drug-free steady state is globally asymptotically stable. If R0>1, 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 R0=1 by analysing the local asymptotic stability and global attractivity.