Optimal Control and Cost‐Effectiveness Analysis of Strategies for Pneumonia Transmission Dynamics

ABSTRACT In epidemiological modeling, cost‐effectiveness analysis is an important tool for identifying efficient strategies to prevent the most infections at the lowest implementation cost. We develop an optimal control model for pneumonia transmission dynamics, incorporating four interventions: vaccination, prevention, treatment, and revaccination. We derive the reproduction number for the model and conduct a sensitivity analysis with respect to various parameters. We establish the existence of optimal controls and determine the corresponding parameter values. Furthermore, we apply the forward fourth‐order Runge–Kutta method and the backward sweep algorithm to evaluate selected combinations of interventions: Strategy A (a combination of vaccination and prevention), Strategy B (a combination of vaccination and treatment), Strategy C (a combination of prevention and treatment), Strategy D (a combination of vaccination and revaccination), Strategy E (a combination of vaccination, prevention, and treatment), Strategy F (a combination of vaccination, prevention, and revaccination), Strategy G (a combination of vaccination, treatment, and revaccination), and Strategy H (a combination of all four controls). Our results show that the strategy combining all four controls is the most effective, with an efficiency index of . However, combining vaccination and prevention is the most cost‐effective strategy, based on average and incremental cost‐effectiveness ratios. This study provides insights for policymakers to prioritize prevention, treatment, vaccination, and revaccination strategies for optimal resource allocation.