Stability Analysis of a Reaction-Diffusion Heroin Epidemic Model

Abstract EN

A reaction-diffusion (R-D) heroin epidemic model with relapse and permanent immunization is formulated.

We use the basic reproduction number R0 to determine the global dynamics of the models.

For both the ordinary differential equation (ODE) model and the R-D model, it is shown that the drug-free equilibrium is globally asymptotically stable if R0≤1, and if R0>1, the drug-addiction equilibrium is globally asymptotically stable.

Some numerical simulations are also carried out to illustrate our analytical results.