Random and chaotic oscillations in a model of childhood epidemics caused by seasonal variations of the contact rate

We consider an alternative approach to a standard model for seasonal oscillations of childhood infections by introducing a noisy variation of control parameter instead of periodic one. Chaotic and noise-induced oscillations are compared and the problem of distinguishing between these two kinds of oscillations is addressed. In a certain range of the action frequencies the synchronization of noise-induced oscillations takes place in the sense that the mean frequency of the oscillations becomes close to the action frequency. We demonstrate also the effect of synchronization between two interacting populations.