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

Annual deaths from scarlet fever in Liverpool, UK during 1848-1900 have bee n used as a model system for studying the historical dynamics of the epidem ics. Mathematical models are developed which include the growth of the popu lation and the death rate from scarlet fever. Time-series analysis of the r esults shows that there were two distinct phases to the disease (i) 1848-18 80: regular epidemics (wavelength = 3.7 years) consistent with the system b eing driven by an oscillation in the transmission coefficient (delta beta) at its resonant frequency, probably associated with dry conditions in winte r (ii) 1880-1900: an undriven SEIR system with a falling endemic level and decaying epidemics. This period was associated with improved nutritive leve ls. There is also evidence from time-series analysis that raised wheat pric es in pregnancy caused increased susceptibility in the subsequent children. The pattern of epidemics and the demographic characteristics of the popula tion can be replicated in the modelling which provides insights into the de tailed epidemiology of scarlet fever in this community in the 19th century.