We formulate and analyze a general diffusive host-pathogen model with an incubation period and nonlocal infections in a spatially heterogeneous environment. The model system is partially degenerate and the solution map is not compact. We first prove that the solutions of the model exist globally and are ultimately bounded. Next, we define the basic reproduction number R0 as the spectral radius of the sum of two next generation operators corresponding to direct and indirect infection modes, and prove that R0 is decreasing with respect to the incubation period and the diffusion coefficient of infectious hosts under some conditions. Finally, we demonstrate that the model system possesses a global attractor, and explore the global dynamics of the system. Especially, we show that the infection-free steady state is globally asymptotically stable if R0≤1. On the other hand, if R0>1, then the infection will persist and the model system admits at least one positive steady state. For spatial homogeneous system, global asymptotic stability of the positive steady state is proved via Lyapunov functional technique. Numerical simulation is conducted to explore singular perturbation phenomenon when the diffusion coefficients approach zero. We observe that the diffusion will not only spread the infection to the low-risk region, but it may also increase the infection level in the high-risk region.