Fractional-Order Optimal Control Strategies for Two-Patch Malaria Transmission Dynamics

Malaria is a vector-borne infectious disease, particularly found in tropical and subtropical regions, where its transmission is driven by the bite of Anopheles mosquitoes. To explore the malaria transmission dynamics between two patches with varying degrees of endemicity, we developed and analyzed a two-patch Atangana-Baleanu fractional-order malaria model that incorporates patch-specific optimal controls: treated mosquito nets, antimalaria drugs, and insecticide. We established nonnegativity and bounded solutions, confirming the model’s mathematical and epidemiological well-posedness. The next-generation matrix technique was employed to calculate the basic reproduction number. The stability analysis indicated that the malaria-free equilibrium is locally and globally asymptotically stable when R0m 1. Actual data on the prevalence of malaria in Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025 were used to validate the model. Numerical simulations indicate that human mobility significantly influences the geographical spread of malaria, while temperature variability notably affects mosquito biting and mortality rates. Furthermore, as fractional orders decrease from one, the spread of the endemic slows. Hence, by applying optimal control, we examined the effectiveness of patch-specific, time-dependent interventions. Results demonstrate that the combined implementation of treated mosquito nets, antimalaria drugs, and insecticide spraying significantly reduces malaria prevalence in both patches, underscoring the importance of integrated, localized intervention strategies. The main novelty lies in the fusion of fractional-order dynamics, spatial heterogeneity (two patches and temperature variability), real-data validation, and patch-specific optimal controls, which collectively provide a more realistic and policy-relevant framework than traditional malaria models that focus on a single homogeneous population.