Optimal Control Strategies for Two-Patch Malaria Transmission Model

Malaria remains a major vector-borne infectious disease, particularly in tropical and subtropical places, where Anopheles mosquito bites are the primary means of transmission. Human mobility plays a crucial role in influencing the geographical distribution of malaria, whereas temperature variations significantly affect mosquito biting behavior and mortality rates. To control malaria transmission across two patches with varying degrees of endemicity, we proposed and analyzed a two-patch compartmental model that includes patch-specific optimal controls, such as treated mosquito nets, insecticide spraying, and antimalaria drugs. We first established that the model solutions remain bounded and nonnegative, thereby confirming the mathematical and epidemiological validity of the model. Using the next-generation matrix technique, we computed the basic reproduction number, R0m. It is critically dependent on both temperature variability and human movement. Stability analysis indicates that the malaria-free equilibrium point is both locally and globally asymptotically stable when R0m