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Journal of Applied Nonlinear Dynamics 12(1) (2023) 53--73 | DOI:10.5890/JAND.2023.03.004

O. D. Makinde$^{1}$, J. O. Akanni$^{2,3}$, A. Abidemi$^{4}$

$^{1}$ Faculty of Military Science, Stellenbosch University, South Africa

$^{2}$ Department of Mathematical and Computing Sciences, Koladaisi University Ibadan, Oyo State, Nigeria

$^{3}$ Department of Mathematics, Universitas Airlangga, Kampus C Mulyorejo Surabaya 60115, Indonesia

$^{4}$ Department of Mathematical Sciences, Federal University of Technology, Akure, P.M.B. 704, Ondo State, Nigeria

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Abstract

The problem of illicit drug use with its associated hazardous effects on social behaviour and human population dynamics require an intervention. In this study, a compartmental deterministic model for the dynamics of illicit drug use student population is proposed and analysed. The illicit drug use threshold, $\mathcal R_0$, associated with the model is computed. The Centre Manifold Theorem is used to establish bifurcation phenomenon. By constructing suitable Lyapunov functions, the global asymptotic stability of the illicit drug-free and illicit drug-present equilibria exhibits by the model is established. It is shown that the illicit drug-free equilibrium is globally asymptotically stable if $\mathcal R_0<1$, otherwise the illicit drug-present equilibrium is globally asymptotically stable. Sensitivity analysis is performed to gain insight into how the model parameters contribute to the dynamics of illicit drug use student population.

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