Mathematical Model on Illicit Substance Use Among Students of Tertiary Institutions in Nigeria

Abstract

The global challenge of dismissal, disability and death of tertiary institution students are attributable to illicit substance use with its addiction. This has become a significant threat to the health and security of people in developed and developing countries. The goal of this research is to formulate a mathematical model for illicit substance (drug) use and addiction. Some control with relevant aspects was considered, which includes psychological, educational, biological and social aspects, as it affects students in tertiary institutions of learning across Nigeria. The model equations were first transformed to obtain the basic reproduction number Ro. The model exhibits the drug-free equilibrium state. The model is analyzed for the existence and stability of the drug-free equilibrium state and endemic equilibrium. In this work, it was established that a drug-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number Ro < 1 and the threshold requirements are met. According to the findings, behavioral modification should be
included in the treatment rates with controls in order to lower the rate of psychotropic substance use among students in higher institutions. In addition, students were considered in the formulation of preventive models that uses education and other control strategies with counselling to achieve behavioural change and reduce illicit substance use among the students of the Nigeria tertiary
institutions