Stability Analysis of Drug Abuse and Drug – Related Crime Mathematical Model

Abstract

Drug abuse is the production, traffic and illicit use of drugs for the purpose of
creating pleasurable effects on the brain. Numerous countries have been
challenged with war against the distressing growth of drug abuse since it
possesses morbidity, mortality and substantial socio-economic impact through
its neuro-psychological effects on quality of life of the victims. Thus, in this
study, a mathematical model on the transmission dynamics of drug abuse and
its related crime was formulated and analyzed. The basic reproduction number
Ro for each model is calculated by using the next generation method and
conditions for elimination or persistence of drug abuse and its related crime are
determined. Stability analysis shows that whenever Ro> 1, the drug free
equilibrium is unstable. The result shows that the menace of drug abuse and its
related crime can be eradicated when the reproduction number is less than
unity and continue to persist when the reproduction number exceed unity.