Mathematical Model and Analysis of Drug Addiction among Adolescent’s Populace in Nigeria

Abstract

Drug addiction has become a menace especially among adolescents which has massively contributed to the social vices perpetrated by youths in Nigeria. We constructed a five-compartment model to explain the transmission dynamics of addiction leading to a non-linear deterministic equation. The next generation approach was employed to obtain the basic reproduction number (R_0). The drug free equilibrium point was obtained and showed to be locally asymptotically stable when the threshold quantity is less than one. A suitable Lyapunov function was constructed for the global stability which was found to be globally asymptotically stable. Sensitivity analysis was conducted to ascertain the behavior of the various parameters on the threshold quantity to deduce a suitable intervention strategy. Numerical simulations are carried out, the analysis is discussed, and the results are presented in graphical form.

Keywords: Addiction, model, drug, stability, basic reproduction number, sensitivity analysis.