Analysis of a mathematical model of the population dynamics of drug addiction among youths

Abstract

Drug addiction amongst youths has been identified as one of the global menace that has affected negatively the development and productivity of young people which has come to stay from time pass to the present day and has resulted to various behavioural disorder such as criminality, psychiatric issues and death. In this paper, a 5 sub-class model is formulated to analyze the population dynamics of drug addiction among youths and the effect of addiction on their development and productivity towards contributing their quota to the human population. The model was developed using ordinary differential equations approach. It was determined that the basic reproduction number which is a vital tool for measuring the impact of drug addiction in human was obtained using the next generation operator method. Stability analysis was carried out and it was discovered that drug-free equilibrium exists and it was shown to be locally and globally asymptotically stable whenever effective basic reproduction number is less than one; and unstable whenever effective basic reproduction number is greater than one. It was discovered that drug abuse persisted among youths and are both locally and globally asymptotically stable whenever effective basic reproduction number is greater than one and unstable whenever effective basic reproduction number is less than one.