Reaction–Diffusion Malaria Model in Heterogeneous Environments

Malaria is a vector‐borne infectious disease primarily found in tropical and subtropical regions, where its transmission is driven by the bite of Anopheles mosquitoes. To explore the spread of malaria between two interconnected patches with varying degrees of endemicity, we developed and examined a reaction–diffusion model that incorporates the combined effects of temperature variability, malaria relapse, human diffusion, and behavioral change through awareness campaigns. We established the non‐negativity and boundedness of solutions. Next‐generation matrix techniques were employed to calculate the basic reproduction number. The stability analysis indicated that the malaria‐free equilibrium is locally and globally asymptotically stable when , but becomes unstable when . Reported case data on malaria in Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025 were used to validate the model. Our findings reveal that human mobility significantly influences the geographical spread of malaria, while temperature variability notably affects mosquito biting and mortality rates. Additionally, relapse can sustain malaria transmission within the community. However, behavioral changes such as draining standing water, improving sanitation, and promoting awareness of malaria prevention can significantly reduce disease transmission and improve public health outcomes. The novelty is that, in contrast to previous models that consider only one or two factors, our model uniquely integrates temperature variability, human movement, disease relapse, and behavioral change within a single reaction–diffusion framework, validated using reported malaria case data from Ethiopia.