Dynamical Behavior of a Heroin Epidemic Model With a Hypothesized Vaccine

ABSTRACT Heroin abuse has reached epidemic proportions globally. Recent advancements in vaccine development‐particularly a novel candidate shown in clinical trials to inhibit heroin‐induced euphoria‐highlight the potential of immunotherapy as a future cornerstone for addiction treatment. To elucidate the transmission dynamics of heroin use and evaluate the prophylactic impact of vaccination, we formulate an epidemic model incorporating a heroin vaccine. Leveraging methodologies from differential equations and epidemiological modeling, we derive the basic reproduction number and rigorously analyze the existence and stability criteria of system equilibria. Notably, the vaccine‐free subsystem exhibits backward bifurcation, whereas the heroin‐persistent equilibrium attains global asymptotic stability when under specified conditions. Furthermore, numerical simulations underscore the critical role of heroin vaccination in curbing addiction propagation, providing actionable insights for public health strategies.