The basic reproduction number and its computation formulae are established for epidemic models with reaction-diffusion structures. It is proved that the basic reproduction number provides the threshold value for disease invasion in the sense that the disease-free steady state is asymptotically stable if the basic reproduction number is less than unity and the disease is uniformly persistent if it is greater than unity. On the basis of these theoretical results, three epidemic models for rabies, lyme disease and West Nile transmissions are analyzed to reveal the better strategies for these diseases. With the aid of numerical simulations, we find that the reduction of heterogenous infection is beneficial because the more heterogenous infection leads to the higher value of basic reproduction numbers. Moreover, influences from spatial configurations of disease infection and diffusion coefficients are investigated. This is a joint work with Xiaoqiang Zhao.