In order to investigate the influences of vaccines, water currents, diffusion rates and spatial heterogeneity on the transmission of water-borne infectious diseases, a SVIRS-B reaction-convection-diffusion model is constructed. First, the fitness of the model and the existence of the global attractor are investigated. Second, the basic reproduction number \({\cal R}_0\) , which describes the extinction and persistence of the disease is obtained, this ensures that the disease-free steady state is globally asymptotically stable when \({\cal R}_0 < 1\) ; if \({\cal R}_0 > 1\) , the disease is uniformly persistent and the model allows for at least an endemic steady state. Furthermore, the asymptotic behavior of the disease-free steady state in the absence of the convection term is discussed for \({\cal R}_0 = 1\) . In addition, in the case of neglecting water convection, the global asymptotic stability of various steady states for the model are obtained in the homogeneous environment. Finally, some numerical simulations illustrate the main theoretical results and reveal some interesting problems, such as the effects of parameters on the spatial and temporal distribution of these diseases.
