Spatial Propagation for an Epidemic Model in a Patchy Environment

This paper investigates the propagation dynamics for an epidemic model with nonlinear incidence rates in a patchy environment. Giving a general setting of the nonlinear incidence rates (monotone or non-monotone), we establish a framework that provides a complete characterization on the existence, non-existence and minimal wave speed of traveling waves which describe the evolution of disease starting from initial disease-free state to final disease-free state. In addition, we obtain the exponential decay rates of infected waves, which reveal that the number of infected individuals increases exponentially when the disease breaks out and decreases exponentially when the disease declines toward extinction. Our results solve the propagation problem for a wide range of spatial discrete epidemic models.