Optimal Control of an Age-Structured Malaria Transmission Model With Imperfect Vaccination

Malaria remains a major global health threat, with the World Health Organization estimating approximately 282 million cases and 610,000 deaths in 2024. To improve the design of vaccination campaigns, we developed an age-structured partial differential equation (PDE) model for malaria transmission that incorporates the imperfect nature of available vaccines. We performed calibration of the PDE-based transmission model using age-stratified epidemiological data from the Ilu Aba Bor Zone, Oromia, Ethiopia. This process involved discretizing the continuous age-structured PDEs into a system of ordinary differential equations (ODEs) structured by age cohorts, enabling the estimation of locally relevant transmission parameters from routine surveillance data. We then formulated and solved an optimal control problem where the vaccination rate is a control function, ζt,a, dependent on both time t and age a, with the objective of minimizing the total economic burden of disease and vaccination costs. Using Pontryagin's maximum principle, we derive the optimality system and characterize the time–age-dependent vaccination strategy. Numerical simulations, parameterized with the data-informed estimates, demonstrate that the optimal strategy dynamically prioritizes young children (ages 0–4) for sustained vaccination while strategically timing efforts for other key groups, a policy proven to be significantly more cost-effective than a uniform approach. Furthermore, our analysis quantifies the price of vaccine imperfection, showing how waning immunity substantially increases the cost and effort required for disease control. By integrating rigorous mathematical modeling with local epidemiological data, this work provides a robust, evidence-based foundation for designing targeted, resource-efficient malaria vaccination programs adapted to the demographic and transmission characteristics of endemic regions.