(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this article, we propose a comprehensive mathematical model that investigates the dynamics of HIV/AIDS transmission, concentrating on two distinct groups: males and females. Within this theoretical framework, seven classes of individuals are considered for each gender. We compute the basic reproduction number R_0, which is crucial to determine the risk of disease transmission among these populations. Furthermore, Routh-Hurwitz criterion is used in stability analysis of disease-free and endemic equilibrium points. The stability analysis of the model provides that at the disease-free equilibrium point the system is locally asymptotically stable when R_0<1, and if R_0>1 the system is locally asymptotically unstable at the endemic equilibrium point. Additionally, the sensitivity of both reproduction number and the state variables with the key parameters are explored in order to revealing the most influential parameters that affect the disease transmission. This study develops an optimal control framework incorporating prevention, screening, and treatment interventions to combat HIV/AIDS transmission in gender-stratified populations. Using fourth-order Runge-Kutta methods implemented in MATLAB, we numerically solve the control system and simulate population dynamics under various intervention scenarios. Our results demonstrate that the combined implementation of all three interventions yields superior infection reduction compared to isolated measures, with significant decreases in prevalence rates observed for both genders. These findings provide quantitative evidence for public health decision-making, offering both a validated mathematical tool for epidemic modeling and practical insights for optimizing resource allocation in HIV/AIDS control programs. The framework advances current methodologies by systematically evaluating intervention effectiveness while accounting for gender-specific transmission dynamics.