Spatial behavior of an epidemic model with migration

It was reported that there are traveling patterns in the spatiotemporal data of epidemics (Cummings et al., Nature 427:344, 2004; Grenfell et al., Nature 414:716, 2001). To well understand the mechanism, we present a spatial epidemic model with migration, which means that the individuals exhibit a correlated motion toward certain direction, and obtain traveling pattern. Our results may be helpful to understand the mechanism of the spatiotemporal epidemics and have potential application of control of the epidemics.