Stability Analysis of a Reaction-Diffusion Heroin Epidemic Model. (8th June 2020) - Zhang, Liang; Xing, Yifan
Abstract : A reaction-diffusion (R-D) heroin epidemic model with relapse and permanent immunization is formulated. We use the basic reproduction number R 0 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 R 0 ≤ 1, and if R 0 > 1, the drug-addiction equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results.