Journal of Advances in Mathematics and Computer Science

HIV/AIDS remains a significant public health concern, especially in regions where drug abuse is prevalent. Drug abuse facilitates HIV transmission through behaviours such as needle sharing and unsafe sexual practices. In this study, a mathematical model was formulated to investigate the co-dynamics of HIV/AIDS and drug abuse within a population. The model consists of seven compartments: susceptible individuals, protected individuals, HIV-infected individuals, drug abusers, dual-infected individuals, those under HIV treatment, and those undergoing rehabilitation. The model incorporates protection mechanisms and rehabilitation efforts aimed at controlling both epidemics. The basic reproduction numbers R₀ were derived using the Next Generation Matrix method to assess the threshold conditions for disease spread or elimination. Analytical results showed that the disease-free equilibrium is locally asymptotically stable when R_C < 1, indicating that both HIV and drug abuse can be controlled under appropriate interventions. Numerical simulations using Maple software further supported the analytical findings. An increase in protection and rehabilitation rates significantly reduced the number of drug abusers, HIV-infected individuals, and co-infections. These results emphasize the critical role of enhancing protection strategies and rehabilitation programs. The study highlights the importance of integrated public health interventions to effectively mitigate the dual burden of HIV/AIDS and drug abuse.