OPTIMAL CONTROL ANALYSIS OF AN AGE-STRUCTURED MODEL OF HIV/AIDS TRANSMISSION DYNAMICS

Optimal control analysis is a mathematical approach used to determine the best combination, timing, and intensity of interventions given to curb the spread of a disease over time, while considering both the disease transmission and the costs of interventions. In this study, an age-structured mathematical model for HIV/AIDS transmission dynamics in Nigeria has been formulated and analyzed. The model incorporates two distinct age classes: immature susceptibles (children under 15 years) and mature susceptibles (adults aged 15-64 years), giving rise to a system of twelve ordinary differential equations. The basic reproduction number R0 was derived using the next-generation matrix method and computed as R0>1, indicating persistent disease transmission without interventions. Optimal control characterization through Pontryagin’s maximum principle and numerical simulations over a 20-year horizon demonstrated that aggressive combined controls reduce the effective reproduction number to 0.41 and decrease peak infections by over 93%. Cost-effectiveness analysis revealed that adult prevention contributes approximately 32% of total infection reduction. The findings provide evidence-based guidance for public health policy, recommending prioritized allocation of resources toward adult prevention interventions and the implementation of combination strategies integrating prevention, screening, and treatment. This research contributes to the advancement of age-structured epidemiological modeling and supports the global initiative to end the AIDS epidemic by 2030.