We considered the spread of exposed and infectious populations in a contact mode of the propagation of the disease in which the populations have only local motions. The corresponding analytical solutions are obtained and the solution shows a propagating waveof asymmetric shape. We compared these analyticalsolutions for the different ranges of parameters. We show that the dynamics of the SEIR model is slower
than that of an SIR model, and that the total proportion
of infectious cases is substantially smaller. Although
it is not really surprising per-se, as the transition
through the additional exposed class takes time, it is
real progress to be able to quantify the differences,
especially as it may allow curative measures to be
decided in order to limit an epidemic outburst.