Variola minor in Braganca Paulista county, 1956: a trend-surface analysis

Trend-surface analysis (TSA), a form of polynomial regression used in geology, ecology and geography, was applied to analysis of the spread of an epidemic of variola minor in a small Brazilian city. Cubic surfaces gave a generalized map of the space-time distribution of the epidemic, allowing those parts of the city to be identified where variola minor was spreading rapidly or slowly. The epidemic spread relatively quickly over the core area of the city, especially to the peripherally located household dwellings in a northeast to south-west direction. The dwellings of adults and pre-school children introducing the disease into their households broadly followed the overall pattern. School child introductory cases from a southern-located school yielded a saddle-shaped contour pattern, centered about the school; but this pattern was not repeated for the school serving the northern half of the city, which showed a ridge-shaped pattern dipping toward the west. Cubic surfaces for the influence of certain household and individual characteristics were investigated, but showed only week trends. The nearest match to the bowl-shaped overall pattern of introductory dates was provided by the vaccination level of the households. From this application, it appears that TSA permits the identification of regional trends in an objective manner and gives a quantitative measure of the importance of these regional trends in terms of the overall variation in the spatial pattern.