Synergistic malaria control through memory effects, seasonal awareness, and multi-strategy optimization in a fractional-order modeling framework

Malaria remains a persistent global health challenge despite long-standing control efforts, with transmission dynamics complicated by human behavioral adaptation and seasonal patterns. We develop an advanced mathematical framework that captures how community awareness, influenced by seasonal factors, affects malaria spread and control. We use fractional-order calculus with Caputo derivatives to model memory effects in disease progression, creating a compartmental system that considers aware and unaware human populations alongside mosquito vectors and a dynamic seasonal awareness variable. Our approach innovatively integrates three distinct advancements: (1) fractional derivatives for realistic memory effects, (2) seasonal awareness as an evolving state responding to infection prevalence, and (3) multi-strategy optimal control analysis of four interventions. Our main contributions include deriving a novel weighted susceptibility parameter quantifying awareness impact, demonstrating context-dependent parameter importance through sensitivity analysis, and numerically quantifying intervention synergy. Our findings reveal that reducing mosquito populations remains the most powerful single intervention, while integrated strategies combining vector control, treatment, awareness campaigns, and preventive measures achieve exceptional effectiveness, reducing infections by approximately 96% and providing a robust mathematical foundation for designing comprehensive malaria control programs.