Scarlet Fever Dynamics in 19th and 20th Century London

Weekly scarlet fever (SF) mortality records for London, UK, from 1842 to 1939, together with notified case records from 1901 to 1939, reveal a strong annual epidemic pattern with peak prevalence in the autumn. In addition to the annual epidemic pattern, this long time series reveals a cyclical envelope with a period that lengthened over the decades. In particular, the period of the envelope increased from about four years to about eight years between 1880 and 1920, coinciding with a dramatic decline in pre-antibiotic-era SF deaths (from about 2300/yr to about 80/yr). We quantify the spectral features of the SF time series using a wavelet transform, and attempt to explain why the frequency structure changed over time, using a mechanistic mathematical model of SF transmission dynamics. We estimate the parameters of the model in part from the literature and in part by fitting mortality and incidence jointly. We use a mechanistic transition analysis (considering both attractors and transients in model solutions) to relate the observed changes in frequency structure to our estimated changes in model parameters. We find that almost all spectral evolution in the time series can be explained by changes in the effective reproduction number and the amplitude of seasonal forcing. These changes reflect observed variation in birth rates together with inferred changes in transmission, which may in part have arisen through pathogen evolution.