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 thegeneral 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, adeterministic model for drugs and substance abuse (DSA) driven by light drug abusers (LDA) and heavy drugabusers (HDA) was proposed. The basic reproduction number R0; , the foundation upon which the model’sstability 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 unstableif R0 > 1. The global stability of both DFE and drugs endemic equilibrium (DEE) are explored by utilizingLyapunov functions. The bifurcation analysis was carried out using the center manifold theorem, where themethod utilized by Castilo-Chavez and Song was implemented and revealed that the rate of drug reinitiationdrove backward bifurcation. The contribution of the important parameters to DSA are investigated, andresults are presented graphically. Results from the simulation revealed that delayed exposure of the youth todrugs increased identification and treatment of the LDA and HDA, which would curtail DSA menace in Kenya.