Modeling the syndemic dynamics of tobacco use and methamphetamine abuse

Nicotine products are frequently co-abused with psychostimulants such as methamphetamine, though the mechanisms sustaining this syndemic remain unclear. Here, we model and analyze a nonlinear system of ordinary differential equations to explain the co-dynamics of tobacco smoking and methamphetamine abuse. Mathematically, the model is revealed to be well posed, admitting the existence of an abuse free equilibrium and multiple substance abuse persistent equilibria. Using the next generation matrix approach, the threshold quantity R₀ is derived, and center manifold theory is employed to show that the substance abuse persistent equilibrium A^∗ is locally asymptotically stable when R₀>1 but close to unity. Numerical simulations indicate that tobacco use acts as a gateway that amplifies initiation into methamphetamine abuse, and that enhanced treatment uptake substantially reduces co-abuser prevalence while increasing recovery levels. The study highlights the importance of integrated prevention and treatment strategies that jointly target tobacco use, access to rehabilitation, and relapse control in curbing the tobacco–methamphetamine syndemic.