Mathematical Analysis of Drug and Substance Abuse Model With Treatment and Policing

On the global arena, drug and substance abuse (DSA) problem has caused unprecedented suffering. The number of the youth and adult population developing addictions has been on a steady rise, according to the United Nations Office on Drugs and Crime (UNODC) report. A new mathematical model incorporating the impact of policing and rehabilitation on proliferation of DSA in the community is designed and examined in this research. This study postulates that the propagation of DSA is comparable to that of horrendous contagious disease. The effective reproduction number R0 of the proposed deterministic model provides the substratum for stability analysis. From the analysis, the DSA-free equilibrium (DSAFE) is corroborated to be locally asymptotically stable when R0 1. The local stability of DSA endemic equilibrium (DSAEE) is explored by employing the centre manifold technique. The study rules out the possibility of occurrence of backward bifurcation. Using Python software, various simulation scenarios were run in order to correlate the outcomes with the analytical findings. The simulation results show that increasing the rate at which light drug abusers (LDAs) and heavy drug abusers (HDAs) are identified and placed under structured treatment and therapy, as well as proactive response by intercepting and dismantling trafficking networks via efficacious law enforcement, would adversely diminish drug abuse menace not only in Kenya but in the world at large.