This paper delves into the dynamics of a spatial eco-epidemiological system with disease spread within the predator population in open advective environments. The disease-free subsystem is first discussed, and the net reproductive rate $ R_P $ is established to determine whether the predator can invade successfully. The impacts of advection rate on $ R_P $ are also discussed. Then for the scenario of successful invasion of the predator, sufficient conditions for the prevalence of disease and the local stability of disease-free attractor are obtained by dint of persistence theory and comparison theorem. Finally, we present a special numerical example, in which the basic reproduction ratio $ R_0 $ of the disease is established in the absence or presence of periodic perturbation. Our theoretical and numerical results both indicate that the advection rate in an intermediate interval can favor the coexistence of prey and healthy predator as well as the eradication of disease.

We propose a reaction-diffusion model to describe the interactive wild and sterile mosquito populations in spatially heterogeneous environments, where the vital dynamics of mosquito populations, e.g., offspring produced per mate, the death rates, the amount of releasing sterile mosquitoes, depend on its location habits and the distribution of wild mosquito populations. First, we show the model may present multiple positive steady states with either Neumann or Dirichlet boundary conditions. Then we investigate the interactive dynamics of mosquito populations with the different initial data. Our results show that wild mosquitoes can be eradicated or suppressed within a certain range with different releasing amounts. Finally, numerical simulations further show that the spatial variability environment within the habitat may play a crucial role in extirpating wild mosquito populations in the context of the sterile insect techniques (SIT).