Spatio-temporal synchronization of recurrent epidemics.

Long-term spatio-temporal datasets of disease incidences have made it clear that many recurring epidemics, especially childhood infections, tend to synchronize in-phase across suburbs. In some special cases, epidemics between suburbs have been found to oscillate in an out-of-phase ('antiphase') relationship for lengthy periods. Here, we use modelling techniques to help explain the presence of in-phase and antiphase synchronization. The nonlinearity of the epidemic dynamics is often such that the intensity of the outbreak influences the phase of the oscillation thereby introducing 'shear', a factor that is found to be important for generating antiphase synchronization. By contrast, the coupling between suburbs via the immigration of infectives tends to enhance in-phase synchronization. The emerging synchronization depends delicately on these opposite factors. We use theoretical results from continuous time models to provide a framework for understanding the relationship between synchronization patterns for different model structures.