Global dynamics of a heroin epidemic model with age structure and nonlinear incidence

A heroin model with nonlinear incidence rate and age structure is investigated. The basic reproduction number is determined whether or not a heroin epidemic breaks out. By employing the Lyapunov functionals, the drug-free equilibrium is globally asymptotically stable if R-0 <= 1; while the drug spread equilibrium is also globally asymptotically stable if R-0 > 1. Our results imply that improving detected rates and drawing up the efficient prevention play more important role than increasing the treatment for drug users.