Inferring the causes of the three waves of the 1918 influenza pandemic in England and Wales

Abstract

Past influenza pandemics appear to be characterized by multiple waves of incidence, but the mechanisms that account for this phenomenon remain unclear. We propose a simple epidemic model, which incorporates three factors that might contribute to the generation of multiple waves: (i) schools opening and closing, (ii) temperature changes during the outbreak, and (iii) changes in human behaviour in response to the outbreak. We fit this model to the reported influenza mortality during the 1918 pandemic in 334 UK administrative units and estimate the epidemiological parameters. We then use information criteria to evaluate how well these three factors explain the observed patterns of mortality. Our results indicate that all three factors are important but that behavioural responses had the largest effect. The parameter values that produce the best fit are biologically reasonable and yield epidemiological dynamics that match the observed data well.

Keywords: Spanish flu; behavioural response; iterated filtering; pandemic influenza; school closure; weather.

Figure 1.

Three pandemic waves swept the UK during 1918–1919. The 334 administrative units that we studied within England and Wales are marked on the map (a); the largest 12 cities are identified by name and with solid (red) dots (the size of which indicate the population size rank of the city). The intensity plot (b) shows the spatio-temporal pattern of the pandemic throughout the country (which we divided into 150 latitudinal bins). Panel (c) on the top right shows the daily central England temperature (CET in °C) and weekly influenza mortality in London (in hundreds). (Online version in colour.)

Figure 2.

Histograms of (a) ΔAIC_c (no behavioural response), (b) ΔAIC_c (no response to school holidays), (c) ΔAIC_c (no response to temperature) for the 50 largest administrative units in England and Wales. A similar figure for all 334 administrative units is given in the electronic supplementary material. (Online version in colour.)

Figure 3.

Simulations compared with observed weekly mortality in 1918. We show: the best model, forced by three factors (human behavioural response, school terms and temperature); a model with no behavioural effects; a model with no school terms and a model with no temperature effects. With estimated parameter values for each model, 1000 simulations were generated (1000 × 46 weekly data points) and displayed using box-plots (one box-plot for each week), compared with observed weekly influenza mortality (46 weeks, solid (red) curve). The three rows show results for three UK cities. The four columns show the four types of model. (Online version in colour.)