Fig 1.
Example of one of the London Bills of Mortality.
Burials by cause for the week ending 26 September 1665, during the Great Plague of London. Five deaths from “Flox and Small-pox” are listed. Photo courtesy of the Public Domain Review, https://publicdomainreview.org/collection/londons-dreadful-visitation-bills-of-mortality.
Fig 2.
Consistency of annual smallpox mortality in London, England, as tabulated by Creighton [36] from annual records, and in this paper from weekly records.
Each panel shows 150 years: 1629–1779 (top panel) and 1780–1930 (bottom panel). Where the tops of stacked bars are white, the annual counts are larger; where the tops are black, the weekly sums are larger. The gap from 1637 to 1646 is due to missing annual bills ([36], p. 437). The data and R script required to reproduce this figure are available at https://github.com/davidearn/London_smallpox.
Fig 3.
London’s population and weekly smallpox deaths, 1664–1930, against the timeline of historical events related to the history of smallpox in England.
The top of the graph shows the population of inner London (dashed) and all of London (solid) as estimated in the London’s population subsection of Data in the main text. The main panel shows weekly smallpox deaths in London in blue and the long-term trend of weekly births in red. Background shading indicates different sources and classifications of disease: 1664–1701, flox and smallpox burials from the London Bills of Mortality (LBoM); 1701–1841, smallpox burials from the LBoM; 1842–1931, smallpox deaths from the Registrar General’s Weekly Returns (RGWRs). The geographical area covered by the RGWR was larger than for the LBoM (see Data for details). Qualitative variolation and vaccination uptake levels are shown with colored bars. Annotation below the main panel shows the timeline of historical events related to smallpox history in England: Black text indicates events that influenced uptake of control measures; brown text indicates events that influenced human behavior; and dark green text is used to highlight reduced data accuracy during the last few decades of the LBoM. The bottom panel shows weekly smallpox deaths normalized by the long-term trend of all-cause deaths (see Fig 4). The trend of normalized smallpox deaths is also shown (heavy black curve). Trends were estimated by Empirical Mode Decomposition (see Methods). Red dots highlight the peaks of the epidemics of 1838 and 1871, the most significant smallpox epidemics of the 19th century. The data and R script required to reproduce this figure are available at https://github.com/davidearn/London_smallpox.
Table 1.
Population of London, England (1550–1931).
Fig 4.
Weekly all-cause deaths in London, England, 1661–1930.
The trend was estimated by Empirical Mode Decomposition (see Methods) applied separately to the periods 1661–1841 and 1842–1930, which correspond to different data sources. Two peaks are cut off in the plot. During the Great Plague of London, deaths reached 8,297 per week in September 1665. During the 1918 influenza pandemic, deaths reached 4,290 per week in November 1918. The data and R script required to reproduce this figure are available at https://github.com/davidearn/London_smallpox.
Fig 5.
Classical Fourier power spectrum of the normalized weekly smallpox mortality time series for London, England, 1664–1930.
Before computing the power spectrum, the time series was square-root transformed and detrended [84]. A standard modified Daniell smoother was used in the computation of the spectrum (see Methods). The data and R script required to reproduce this figure are available at https://github.com/davidearn/London_smallpox.
Fig 6.
Spectral structure and seasonality of smallpox dynamics in London, England, 1664–1930.
Panel A: weekly smallpox deaths normalized by the long-term trend of all-cause deaths. The red dots indicate the epidemic peaks, i.e., the highest value of normalized smallpox mortality during the epidemic year (identified by visual inspection). Panel B: wavelet transform of the normalized weekly smallpox mortality time series (square root-transformed and normalized to unit variance). Colors range from dark blue for low power to dark red for high power. Heavy black curves show the local maxima of wavelet power (squared modulus of wavelet coefficients [89]) at each time. Thin black curves show 95% confidence contours, estimated from 1,000 bootstrapped time series generated by the method of [89]. Medium black curves near the left and right edges show the cone of influence [89,92], below which the calculation of wavelet power is less accurate because it includes edges of the time series that have been zero-padded to make the number of time points a power of 2. The wavelet spectrum was computed using MATLAB code kindly provided by Bernard Cazelles. Panel C: seasonal heat map based on the detrended, square-root transformed, normalized smallpox time series (see Seasonality subsection of Methods). Colors indicate the degree of variation from the global mean of the time series (which is 0 after detrending). Panel D: The epidemic peak times (red dots in Panel A) are displayed with gray dots in the year versus time-of-year plane. The red curve shows the moving average peak week, computed using a window of 21 epidemics. As in Fig 3, variolation and vaccination uptake levels are indicated above Panel A, and the timeline of historical events related to smallpox history in England is shown below Panel D. The data and R script required to reproduce this figure are available at https://github.com/davidearn/London_smallpox.
Fig 7.
Periodicities in the time series of smallpox mortality in London, 1664–1930.
Upper panel: primary spectral peaks, as estimated in previous work [21,48] (based on traditional spectral analysis of annual data), and in this paper (based on a wavelet analysis of weekly data). For the wavelet analysis, all spectral peaks above the threshold used in Fig 6B are shown with red dots; the pink curves underneath are based on visual identification of peaks in Fig 6B. Lower panel: Interepidemic period estimated by the time between successive epidemic peaks. A nine-point (central) moving average of the peak-to-peak intervals is also shown. The data and R script required to reproduce this figure are available at https://github.com/davidearn/London_smallpox.