Ecological boundaries are a key site for the spillover of wildlife pathogens into human and domestic livestock populations. Ebola virus is a zoonotic pathogen that is periodically introduced into humans causing outbreaks of a highly fatal hemorrhagic disease. There is evidence that spillover risk varies seasonally. Here we hypothesize that this seasonality may be due to periodic variations in pathogen-host interactions, host social behaviors, movement and contact rates, and demography. To better understand the dynamics of such a system, we studied a two-patch SIR compartmental model for the spillover of Ebola virus with seasonal and demographic variability. The model is expressed as a system of coupled ordinary differential equations (ODE) with periodic disease transmission and dispersal between supercritical and subcritical patches. The periodic ODE system is generalized to a stochastic Continuous-Time Markov Chain (CTMC) model. The basic reproduction number of the two-patch SIR model is derived at the disease-free equilibrium to illustrate the impact of seasonality and movement on Ebola virus outbreaks. Several numerical examples are investigated. We find that the seasonality strength and human movement are two potentially leading factors that are responsible for the intensity of periodic spillover risk from pathogen reservoirs to human settlement regions.