Chaos and complexity in measles models: A comparative numerical study

Recurrent epidemics of measles in developed countries offer a proving ground for current theories of complicated dynamics in ecological and epidemiological systems. This paper contrasts the basic forced SEIR model for measles with a variety of more complicated and realistic models, showing that variations in seasonal forcing and age-structured mixing patterns can generate a wide range of global dynamics. The well-known chaotic dynamics of the forced SEIR model appear to be absent from more realistic models, suppressed by the buffering effect of a low-risk group of pre-school children. These results, and the variety of measles dynamics seen in real populations with different demographic and geographic patterns, point out the need for age- and spatially-structured measles models and suggest caution in the construction of models for complicated systems.