The present proposal aims to increase our understanding of childhood diseases characterized by recurrent outbreaks. Previous work suggests that many features of these epidemics can be understood in terms of the basic SEIR model for microparasitic infections.It is proposed to extend this finding in two directions: 1 . Spatial Effects. Often it is assumed that populations are infinitely large and that individual cities can be treated as isolated systems. Neither assumption is strictly accurate. I propose to study the consequences of finite populations and coupling. For isolated systems, reduced population size increases the effects of demographic stochasticity, i.e., sampling error. In Monte Carlo simulations, varying population size can induce qualitative changes in the observed dynamics. For systems composed of multiple elements, e.g., several cities, it is conjectured that there are two critical connectance levels: a lower threshold which prevents the disease from dying out, and a higher threshold beyond which epidemics in different locales are synchronized. When, as in the case of measles, the disease exhibits large scale fluctuations, coupling above the second threshold, should lead to its extinction over entire regions. In such cases, persistence of the infection should require intermediate coupling. 2. Predictability. Analyses of data for measles, rubella and, in some cases, mumps, suggests that in the absence of vaccination, these diseases undergo chaotic fluctuations.Theory suggests that there should exist a relationship by which this number of cases in year i can be predicted from the numbers in years i-1 and i-2.- In fact, first order dependence, i.e., X(i) on X(i-1), of the sort predicted is observed. But second order dependence is not. It is believe that this failure results from reporting errors. Calculations will be undertaken to determine the relationship of reporting accuracy to predictability. Comparisons between the new techniques and traditional methods will be undertaken assuming different degrees of accuracy in reporting. Roughly equal effort will be devoted to studying mathematical models and real world epidemics. Although the focus of the proposal is childhood diseases, it is hoped that the results will be applicable to the more general problem of spatio-temporal variation in recurrent infections.
