Age-structured malaria model with temperature-dependent dynamics and optimal control analysis within a partial differential equation framework

Abstract

Malaria remains a significant global health challenge, particularly in sub-Saharan Africa, despite advances in control measures. In 2023, there were an estimated 263 million malaria cases and 597,000 deaths, with most occurring in Africa. This study presents a temperature-dependent, two-class age-structured malaria model using partial differential equations and optimal control strategies to assess their impact on malaria transmission. We analyze the existence and stability of equilibria, determined by the basic reproduction number R0, and demonstrate global stability through Lyapunov functionals. Numerical simulations show the effects of temperature variations and optimal controls on transmission dynamics, providing actionable insights for malaria management. Empirical validation of the model was performed using six years of infection prevalence data from the Jimma zone, revealing an R2 of 0.68 and an adjusted R2 of 0.63, indicating a good fit to observed data. Furthermore, comparison with an existing age-structured malaria model from the literature showed superior predictive accuracy, with our model demonstrating better performance in capturing temperature-dependent malaria trends. These results underscore the robustness and practical relevance of the model, offering improved prediction and control strategies under varying environmental conditions.