Analysis of Substance Abuse Control Model in Nigeria

Abstract

In this research, mathematical modelling of treatment control of substance abuse in Nigeria was carried out. We present a deterministic model for the of control treatment of substance abuse in which impatient and outpatient were both important for the disease control. We calculated the basic reproduction number using next generation matrix method and The analytical results reveal that the substance abuse model is mathematically well-posed and defined within the positive region of the parameter space, Λ. The existence of equilibrium states is established, with both the substance abuse-free equilibrium (SAFE) and the substance abuse-endemic equilibrium (SAEE) found to be locally and asymptotically stable under certain conditions, and unstable otherwise. Furthermore, the global stability analysis of the SAEE indicates that it is asymptotically stable. The study also deduces that the control methods employed can effectively reduce the progression rate of substance abuse. Importantly, the analysis highlights that individual involvement and commitment will play a vital role in the successful control of the substance abuse menace in Nigeria. This study provides valuable insights into the mathematical modelling and analysis of substance abuse dynamics, which can inform the development of effective intervention strategies and policies to address this critical public health challenge in the Nigerian.