Dynamic behavior of a reaction-diffusion dengue model with spatial heterogeneity

Dengue is one of the most prevalent vector-borne viral diseases, which is transmitted through the bite of Aedes mosquitoes (Aedes albopictus). In this study, using the global exponential attraction theory, the dynamic behavior of the dengue model in a spatially heterogeneous environment was studied. The existence and uniqueness of positive global solutions were proven using the semigroup theory. The basic reproduction number was defined using the spectral radius of the next-generation operator. Furthermore, a global exponential attractor set was given, and the results of globally asymptotically stable and disease uniform persistence were obtained for the dengue model. A numerical simulation showed the dynamic behavior and revealed that increasing the diffusion coefficient and spatial heterogeneity rate is beneficial for disease control.