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.

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The phenomenon of drug epidemics has been a global issue in the past decades, causing enormous damages to the physical and mental health of drug users and social well-being. Despite great efforts to curb drug epidemics at the governmental or social level, the total number of drug users has still been on the rise in recent years, along with illicit production and trafficking around the world. Inspired by dynamical epidemic models of infectious disease, a flourishment of promising results has been observed in the exploration of drug epidemic models. In this review, we aim to provide a scoping review of all existing drug epidemic modeling studies, and it has been shown that most studies focused on analyses of theoretical behaviors of the model systems, lacking emphasis on practical applications in real settings. We found that the drug epidemic models were characterized by a longer time scale, no incubation period, no significant prevention vaccines interfered, and population specificity. This review could assist policymakers and public health workers in gaining deeper insights into modeling tools, and help modelers improve their works, thus narrowing gaps between mathematical epidemiology and public health studies.

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