Modelling the dynamics of scarlet fever epidemics in the 19th century

Abstract

Annual deaths from scarlet fever in Liverpool, UK during 1848-1900 have been used as a model system for studying the historical dynamics of the epidemics. Mathematical models are developed which include the growth of the population and the death rate from scarlet fever. Time-series analysis of the results shows that there were two distinct phases to the disease (i) 1848-1880: regular epidemics (wavelength = 3.7 years) consistent with the system being driven by an oscillation in the transmission coefficient (deltabeta) at its resonant frequency, probably associated with dry conditions in winter (ii) 1880-1900: an undriven SEIR system with a falling endemic level and decaying epidemics. This period was associated with improved nutritive levels. There is also evidence from time-series analysis that raised wheat prices in pregnancy caused increased susceptibility in the subsequent children. The pattern of epidemics and the demographic characteristics of the population can be replicated in the modelling which provides insights into the detailed epidemiology of scarlet fever in this community in the 19th century.