Summary: For infectious diseases such as influenza and brucellosis, the susceptibility of a susceptible highly depends on the distance from each adjacent infectious individual. Such a propagation mechanism is often modeled by a nonlocal incidence with a kernel function \(K(x)\), whose support determines the effective infection area. This nonlocal incidence of infection, together with important seasonal factors, leads to a periodic kernel function \(K(t,x)\) and periodic parameters in a diffusive susceptible-infectious-recovered (SIR) model equipped with homogeneous Neumann boundary conditions. We first study the global well-posedness and the dissipativity of solutions. This is followed by the investigation of the global dynamics in terms of the basic reproduction number \(\mathcal{R}_0\) defined to be the spectral radius of the next infection operator. The following results are shown rigorously: (1) If \(\mathcal{R}_0<1\), the disease-free periodic solution is globally asymptotically stable. (2) If \(\mathcal{R}_0>1\), the model is uniformly persistent and admits an endemic periodic solution. When the support size of \(K(t,x)\) tends to 0, the basic reproduction number takes the \(\mathcal{R}_0\) of the local infection model as the limit. Without seasonality, \( \mathcal{R}_0\) and the endemic size of \(I(t)\) (i.e., the total number of infected individuals at time \(t\) in the studied area) both decrease when the support size of \(K(x)\) increases; however, there is no uniform result for the value and time of the disease outbreak peak. We also explore the integrated impact of seasonality and the infection rate \(\beta\) on \(I(t)\). In addition, when the support size of \(K(t,x)\) increases, the time difference between the first peak and the last peak of \(I(t,x)\) decreases, and when the support size of \(K(t,x)\) is large enough, the disease outbreak occurs almost simultaneously in the whole region. Moreover, due to seasonality not all locations experience a major disease outbreak in the early stage of disease transmission when the support size of \(K(t,x)\) is relatively small.