Periodic and aperiodic traveling pulses in population dynamics: An example from the occurrence of epidemic infections

The dynamics of the occurrence of the dengue hemorrhagic fever in the 72 provinces of Thailand is investigated by performing a proper orthogonal decomposition ͑POD͒ on spatiotemporal data. Using this technique, we are able to identify and select the contribution of different modes, selected according to the energy content, to the evolution of the epidemic during 14 years. We found that the phenomenon is characterized by periodic cycles of yearly occurrence characterized by spatial scales of about 420 km. Superimposed on this basic mode, POD analysis is able to reveal the presence of high-energetic aperiodic traveling pulses of the epidemic, which extend spatially for about 510 km from Bangkok.