Substance abuse is one of the major global health and social problems. In view of this, a mathematical model was designed to analyze the dynamics of drug abuse and banditry among population. Necessary conditions for the existence and stability of drug abuse and banditry steady states are derived. The drug abuse and banditry reproduction number is evaluated. A locally asymptotically stable drug abuse and banditry-free equilibrium at the drug abuse and banditry basic reproduction number less than unity is proved via the analysis of characteristic equation. Whereas, the existence of a locally asymptotically stable drug abuse and banditry-present equilibrium is established at the basic reproduction number greater than unity based on the use of center manifold theory of bifurcation. Bifurcation analysis at the threshold, R0 = 1, is investigated. Moreover, the local asymptotic dynamics of the model related to the drug abuse and banditry is showed to exhibit backward bifurcation. In addition, a sensitivity analysis is performed to examine the contributory effects of the model parameters on the spread of the drug abuse and banditry menace with respect to the drug abuse and banditry basic reproduction number.
Digital Object Identifier (DOI)
John Olajide, Akanni
"Asymptotic Stability Of Illicit Drug Dynamics with Banditry Compartment,"
Applied Mathematics & Information Sciences: Vol. 14:
5, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss5/6