Dynamical analysis and optimal control of a reaction-diffusion malaria model with chemotactic and vaccination

The integration of human vaccination into malaria models offers a novel tool for leveraging high-efficacy vaccines like R21/Matrix-M in blocking transmission. Concurrently, incorporating mosquito chemotaxis is critical for simulating the directed movement of vectors that drives spatial hotspot formation. To this end, we develop a novel reactiondiffusion framework integrating both mechanisms. We establish the well-posedness of the model, derive the basic reproduction number R 0 , and analyze the associated threshold dynamics. Furthermore, an optimal control framework is formulated under the assumption of no chemotaxis to minimize the density of infected humans and mosquitoes, and the cost of vaccination, bed-net usage, treatment and insecticide application. Numerical simulations validate the analytical results and reveal that vaccination substantially reduces disease burden, and that increasing chemotaxis induces heterogeneous spatial distribution of mosquitoes, driving their aggregation in areas of high human density. Additionally, in malaria control, strategies must account for geographical heterogeneity to enable spatially targeted interventions that effectively suppress transmission while minimizing operational costs.