Propagation dynamics in a diffusive SIQR model for childhood diseases

This paper is concerned with the propagation dynamics in a diffusive susceptible-infective nonisolated-isolated-removed model that describes the recurrent outbreaks of childhood diseases. To model the spatial-temporal modes on disease spreading, we study the traveling wave solutions and the initial value problem with special decay condition. When the basic reproduction ratio of the corresponding kinetic system is larger than one, we define a threshold that is the minimal wave speed of traveling wave solutions as well as the spreading speed of some components. From the viewpoint of mathematical epidemiology, the threshold is monotone decreasing in the rate at which individuals leave the infective and enter the isolated classes.