Mathematical Modelling of HIV/AIDS Dynamics in Relation to Drug Abuse
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Date
2025-09
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THE CATHOLIC UNIVERSITY OF EASTERN AFRICA
Abstract
This study has investigated the co-dynamics of HIV/AIDS and drug abuse, focusing on how protection strategies and rehabilitation programmes influence transmission. The problem addressed is the strong interaction between drug abuse and HIV spread, particularly in Kenya, where injection drug use and risky behaviours heighten vulnerability to infection. The primary objective of the study was to create and evaluate a mathematical model that integrates protection and rehabilitation as control strategies. Specifically, the study aimed to investigate the stability of disease-free and endemic equilibria, compute basic and control reproduction numbers, conduct sensitivity analysis, and evaluate the impact of interventions through numerical simulations. A deterministic model with seven compartments, founded on ordinary differential equations, was developed and analyzed. The next-generation matrix method was employed to calculate reproduction numbers, while equilibrium stability was evaluated using the Jacobian method, Routh–Hurwitz criteria, and Lyapunov functions. Sensitivity analysis was performed to determine the most significant parameters, and numerical simulations were executed with Maple software. The findings indicated that the disease-free equilibrium is both locally and globally stable when RC < 1, suggesting that HIV/AIDS and drug misuse can be effectively managed with adequate measures. Simulations confirmed that higher protection and rehabilitation rates significantly reduce the prevalence of drug abusers, HIV-infected, and co-infected individuals. Sensitivity analysis highlighted protection and
rehabilitation as the most critical parameters. The study concludes that integrated interventions, combining protection measures with effective rehabilitation, are essential for reducing the dual burden of HIV/AIDS and drug abuse. These findings offer significant insights for policymakers and health practitioners in formulating targeted public health interventions.
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Keywords
Mathematical modelling, HIV/AIDS dynamics, HIV transmission, drug abuse