Mathematical Analysis of Drugs and Substance Abuse in Kenya among the Adolescents

Abstract

It is incontestable that the mortality rate among drugs and substance abusers is higher than that in the
general population. The National Authority for the campaign against alcohol and substance abuse (NACADA)
has painted a grim picture of the incessant rise in the number of youth becoming addicted. In this research, a
deterministic model for drugs and substance abuse (DSA) driven by light drug abusers (LDA) and heavy drug
abusers (HDA) was proposed. The basic reproduction number R0; , the foundation upon which the model’s
stability analysis is established, was determined by utilizing the next-generation matrix (NGM) approach.
The analysis showed that drug-free equilibrium (DFE) is locally asymptotically stable for R0 < 1 and unstable
if R0 > 1. The global stability of both DFE and drugs endemic equilibrium (DEE) are explored by utilizing
Lyapunov functions. The bifurcation analysis was carried out using the center manifold theorem, where the
method utilized by Castilo-Chavez and Song was implemented and revealed that the rate of drug reinitiation
drove backward bifurcation. The contribution of the important parameters to DSA are investigated, and
results are presented graphically. Results from the simulation revealed that delayed exposure of the youth to
drugs increased identification and treatment of the LDA and HDA, which would curtail DSA menace in Kenya.