SPATIAL HETEROGENEITY IN EPIDEMIC MODELS

Spatial heterogeneity is believed to play an important role in the per sistence and dynamics of epidemics of childhood diseases because async hrony between populations within different regions allows global persi stence, even if the disease dies out locally. A simple multi-patch (me tapopulation) model for spatial heterogeneity in epidemics is analysed and we examine conditions under which patches become synchronized. We show that the patches in non-seasonal deterministic models often osci llate in phase for all but the weakest between patch coupling. Synchro nization is also seen for stochastic models, although slightly stronge r coupling is needed to overcome the random effects. We demonstrate th at the inclusion of seasonal forcing in deterministic models can lead to the maintenance of phase differences between patches. Complex dynam ic behaviour is observed in the seasonally forced spatial model, along with the coexistence of many different behaviours. Compared to the no n-spatial model, chaotic solutions are observed for weaker seasonal fo rcing; these solutions have a more realistic minimum number of infecti ves. (C) 1996 Academic Press Limited.