Drug abuse remains one of the major public health issues at the global level. In this article, we propose a drug epidemic model with a complete addiction-rehabilitation-recovery process, which allows the initiation of new users under the influence of drug addicts undergoing treatment and hidden drug addicts. We first conduct qualitative analyses of the dynamical behaviors of the model, including the existence and positivity of the solutions, the basic reproduction number, global asymptotic stabilities of both the drug-free and the drug-persistent equilibria, as well as sensitivity analysis. Then we use the model to predict the drug epidemic in China during 2020-2030. Finally, we numerically simulate the potential impact of intervention strategies on different drug users. The results show that the drug epidemic will decrease significantly during 2020-2030, and the most effective intervention strategy to eliminate drug epidemics is to strengthen the investigation and rehabilitation admission of hidden drug users.
Keywords: China; basic reproduction number; drug epidemic model; numerical simulation; sensitivity; stability.