Global existence of solutions for a mosquito-borne disease model with chemotaxis and spatial diffusion

We propose a mathematical model for mosquito-borne disease transmission incorporating chemotaxis and spatial diffusion. Under Neumann boundary conditions, we establish the global existence of solutions for the proposed system. Specifically, in one-dimensional bounded intervals, we prove the global existence for arbitrary initial data. For higher-dimensional cases, we derive global solvability results to prevent solution blow-up by applying the regularity theory of partial differential equations and properties of the Neumann heat semigroup. Our analysis ensures the well-posedness of the model across different spatial dimensions.