DYNAMICS OF MEASLES EPIDEMICS: SCALING NOISE, DETERMINISM, AND PREDICTABILITY WITH THE TSIR MODEL

Host-pathogen models are essential for designing strategies for managing disease threats to humans, wild animals and domestic animals. The behaviour of these models is greatly affected by the way in which transmission between infected and susceptible hosts is modelled. Since host-pathogen models were first developed at the beginning of the 20th century, the 'mass action' assumption has almost always been used for transmission. Recently, however, it has been suggested that mass action has often been modelled wrongly. Alternative models of transmission are beginning to appear, as are empirical tests of transmission dynamics.

Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual '4- and 10-year cycle' of wildlife are often found. In the proposed spatial model, each local patch sustains a three-level trophic system composed of interacting predators, consumers and vegetation. Populations oscillate regularly and periodically in phase, but with irregular and chaotic peaks together in abundance-twin realistic features that are not found in standard ecological models. In a spatial lattice of patches, only small amounts of local migration are required to induce broad-scale 'phase synchronization, with all populations in the lattice phase-locking to the same collective rhythm. Peak population abundances, however, remain chaotic and largely uncorrelated. Although synchronization is often perceived as being detrimental to spatially structured populations, phase synchronization leads to the emergence of complex chaotic travelling-wave structures which may be crucial for species persistence.