Mathematical Insights into the Spatio-Temporal Dynamics of Vector-Borne Diseases in Tropical Regions

Vector-borne diseases pose a significant public health challenge in tropical regions, where complex interactions between hosts, vectors, and the environment drive epidemic dynamics. In this study, we develop a spatio-temporal mathematical model to describe the spread of such diseases, incorporating population dynamics and spatial–temporal factors affecting pathogen transmission. We conduct a theoretical analysis of the model, proving the existence, uniqueness, and positivity of solutions. Additionally, we examine equilibrium states and key epidemiological parameters, including the basic reproduction number. Our findings provide mathematical insights into epidemic propagation and offer a foundation for designing effective control strategies.