Asian Research Journal of Mathematics

This paper examines how best to control Pneumonia–HIV co-infection by extending an existing deterministic model with treatment interventions for both diseases. It presents the numerical simulation and cost-effectiveness analysis of an optimal control model for Pneumonia-HIV co-infection, building upon a previously formulated deterministic model. The optimal control strategies incorporate Pneumonia treatment and HIV Antiretroviral Therapy to minimize both disease prevalence and control costs. Using Pontryagin’s Maximum Principle, the optimality system was derived and solved numerically using MATLAB. Three control strategies were evaluated: Strategy 1 (Pneumonia treatment only), Strategy 2 (HIV treatment only), and Strategy 3 (combined treatment). The results demonstrate that the combined strategy (Strategy 3) is the most effective in reducing co-infection prevalence. A cost-effectiveness analysis using Incremental Cost-Effectiveness Ratios (ICER) and Infections Averted Ratios (IAR) further confirmed that Strategy 3 is the most cost-effective as it achieves the highest number of infections averted at a lower cost per unit compared to other strategies. The findings show that applying pneumonia treatment alongside antiretroviral therapy produces the greatest reduction in co-infection levels and averts the highest number of cases at a comparatively lower cost. The results highlight the importance of integrated treatment approaches and offer practical guidance for health planners working in settings with limited resources. These findings provide critical insights for public health policymakers in allocating limited resources for managing Pneumonia-HIV co-infection.