A simple model for complex dynamical transitions in epidemics

Dramatic changes in patterns of epidemics have been observed throughout thi s century. For childhood infectious diseases such as measles, the major tra nsitions are between regular cycles and irregular, possibly chaotic epidemi cs, and from regionally synchronized oscillations to complex, spatially inc oherent epidemics. A simple model can explain both kinds of transitions as the consequences of changes in birth and vaccination rates. Measles is a na tural ecological system that exhibits different dynamical transitions at di fferent times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.