Threshold Dynamics and Asymptotic Profiles in a Partially Degenerate Reaction–Diffusion model of Vector‐Borne Diseases With Asymptomatic Infections

ABSTRACT To explore the impact of spatial heterogeneity, population movement inevitability, and asymptomatic infection prevalence on vector‐borne disease transmission, we developed a partially degenerate reaction–diffusion model to characterize pathogen spread between vectors and hosts. Using some subtle estimates and induction methods, the well‐posedness of solutions of this model are established, including the global existence of solutions, ultimate boundedness of solutions, and existence of global compact attractors. Further, by applying the next‐generation operator, we define the basic reproduction number and derive its explicit expression. And then, the critical threshold based on are obtained: for , the disease‐free steady state ( ) is globally asymptotically stable; for , the disease becomes uniformly persistent. Notably, we also establish that the positive steady state ( ) is globally asymptotically stable under conditions of homogeneous environments and when all infections progress through the asymptomatic stage. Furthermore, the asymptotic profiles of the are derived as the diffusion rates approach zero or infinity. The theoretical findings are validated through numerical simulations, which reveal that the mobility of asymptomatic hosts plays a critical role in shaping the spatio‐temporal distribution of infected individuals. Further analysis indicates that the ratio of asymptomatic to symptomatic hosts can induce both risk accumulation and risk‐shifting phenomena. Using the partial rank correlation coefficient (PRCC) method, we identify key parameters that significantly affect the basic reproduction number. Based on these insights, we propose implementing integrated control strategies, including targeted insecticide application, measures to reduce host–vector contact, and improved early screening and management of asymptomatic infections.