Modeling the impact of public health education programs and relapse of the rehabilitees on drug and substance use dynamics

Over the years, substance abuse has predominantly remained a problematic issue on the global scene due to its unprecedented health and societal ramifications. The debilitating effects of drug use have incessantly threatened to ruin the future of the young generation and severely damage the economies of many nations. In this study, the influence of ineffective treatment and antidrug education campaigns on the dynamics of drug spread in a population is investigated using a mathematical model approach. The model is constructed by stratifying the population into seven exclusive compartments: susceptible (S), conscious (C), exposed (E), light drug addicts (LDA) (L), hard drug addicts (HDA) (H), drug addicts under treatment (T), and individuals who quit drug use (Q). By analyzing the dynamical properties of the proposed model, we demonstrated that the drug-free equilibrium point is locally asymptotically stable when the basic reproduction number R 0 is less than one and unstable when it is greater than one. The local and global stability of the drug and substance abuse (DSA) endemic equilibrium is examined using the central manifold technique and the Lyapunov function, respectively. Then, utilizing Python software, we were able to perform the sensitivity analysis and numerical simulations on the model parameters. The results of simulation and sensitivity analysis show that the initiation coefficient β, the effectiveness of awareness campaigns ω, the rate at which the exposed population quits experimenting with drugs γ 1 , and the treatment rate of drug addicts ζ are the most influential parameters of the DSA epidemic. These findings therefore underscore the need for adoption and implementation of progressive control measures not only to reduce DSA initiation through the awareness campaigns but also for early identification of the exposed persons through screening in order to intercept and dissuade them from sliding into addiction.