On a reaction–diffusion system modeling the dengue transmission with nonlocal infections and crowding effects

摘要

In this paper, we intend to understand the influences of the spatial heterogeneity, crowding effect and non-local infection caused by the movements of the latent mosquitoes on the dynamics of dengue transmission. For this purpose, we modify the homogeneous system provided in Esteva and Vargas (1998) to obtain a nonlocal and time-delayed reaction–diffusion system with the Neumann condition on the boundary. Then the basic reproduction number R0 is defined for the model system, and it can be obtained explicitly when all model parameters are constants. Finally, we show that the global threshold dynamics of the model system can be determined by R0.