A Spatiotemporal Framework for Malaria Control Integrating Exposure Heterogeneity and Optimal Strategy Deployment

Abstract

Malaria remains one of the most serious and widespread vector-borne infectious diseases globally, caused by Plasmodium protozoa and transmitted through bites of infected female Anopheles mosquitoes. In this study, we develop a novel integrative bioinformatics-driven deterministic mathematical model to capture the complex transmission dynamics of malaria. Our model distinguishes between homogeneous and heterogeneous exposed human compartments (Ehm, Eht) and explicitly incorporates mosquito population dynamics. The coupled system comprises human compartments SM, Ehm, Eht, IM, HM, RM and mosquito compartments SF , EF , IF . We conduct a thorough stability analysis of the malaria-free equilibrium, evaluating both local and global stability in relation to the basic reproduction number R0. Sensitivity analysis identifies the biting rate αM and infection probability βM as critical parameters driving disease transmission. To assess intervention efficacy, we integrate time-dependent control strategies and formulate an optimal control problem using Pontryagin’s Maximum Principle. The control variables
include bed net usage (m1), medication treatment (m2), and insecticide spraying (m3). Numerical simulations, implemented via a fourth-order Runge-Kutta scheme, demonstrate the effectiveness of these interventions in reducing both exposed and infected populations. Our findings underscore the importance of targeted, time-optimized control measures and validate the utility of combining bioinformatics with mathematical modeling to inform malaria control policies.