Predicting smallpox epidemics: A statistical analysis of two Finnish populations.

We analysis data on death due to smallpox in two subdivided Finish populations, the relatively isolated Åland Islands and the mainland parish of Kitee. The data span a 135-year time period (1750-1885). Logisitic regression and Cox proportional hazards models are used to assess the effects of predictive variables on (1) the probability that an individual subdivision experiences an epidemic and (2) the length of the time period between two epidemics in each subdivision. The predictive variables include population sizes, migration rates, geographic distance, and presence or absence of vaccination. Vaccination was found to be the single most important predicative variable (odds ratio = 6.3 in Åland and 4.4 in Kitee). No other variable were significant predicators in Kitee, while geographic distance was an additional significant predicator in Åland (odds ratio = 1.05). As expected, vaccination and geographic distance were both negatively associated with the probability of epidemic occurrence. The Mantel regression approach was used to evaluate the effects of independent variables on the probability that any two subdivisions experienced the same epidemic. Between-subdivision migration rates were the most important predictive variable here, and population size was an important predictor in Åland but not in Kitee. The differing results in these two populations are explained in terms of differences in ecological setting and social organization.