Geographical Distributions and Spatial Equilibrium in Historical Epidemics of the United States

Abstract

This research examines the geographical distributions of several historical epidemics in the United States and investigates whether they reached a geographical equilibrium, however briefly. An equilibrium distribution over a geographical area, as the end state of a diffusion or spatial contagion process, has definitive mathematical properties. These permit qualitative and quantitative tests that may confirm an equilibrium and identify its characteristics. The analysis uses United States state-level data for several common infectious diseases of the 1950s, and results show geographical equilibrium distributions for several epidemics. These are not predicted by the most commonly used epidemiological models but are consistent with observed geographical disparities in disease prevalence that continued over a number of years in spite of recurrent epidemic cycles and long-term trends.