Patterns of smallpox mortality in London, England, over three centuries

Smallpox is unique among infectious diseases in the degree to which it devastated human populations, its long history of control interventions, and the fact that it has been successfully eradicated. Mortality from smallpox in London, England was carefully documented, weekly, for nearly 300 years, providing a rare and valuable source for the study of ecology and evolution of infectious disease. We describe and analyze smallpox mortality in London from 1664 to 1930. We digitized the weekly records published in the London Bills of Mortality (LBoM) and the Registrar General’s Weekly Returns (RGWRs). We annotated the resulting time series with a sequence of historical events that might have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in reported smallpox mortality changed over decades and centuries; many of these changes in epidemic patterns are correlated with changes in control interventions and public health policies. We also examine how the seasonality of reported smallpox mortality changed from the 17th to 20th centuries in London.

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Regardless of the method selected, please ensure that you provide the individual numerical 102 values that underlie the summary data displayed in the following figure panels as they are 103 essential for readers to assess your analysis and to reproduce it: Figs 1, 2, 3, 4, 5, 6, S1, S2.

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NOTE: the numerical data provided should include all replicates AND the way in which the 105 plotted mean and errors were derived (it should not present only the mean/average values).

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Please also ensure that figure legends in your manuscript include information on where the 107 underlying data can be found, and ensure your supplemental data file/s has a legend. The authors have done a great job in revising the paper. It is much clearer and more 117 tightly written, and presents a very impressive integration of historical and epidemiological 118 literatures. I think it will make a great addition to current debates over the recent evolution 119 of smallpox.

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Thanks very much! 121 I have only minor comments that should be addressed before publication. 122 1. The authors are now perhaps too reticent in attributing causation, especially with re-123 spect to vaccination (page 14/33, lines 431-6). The decline in smallpox deaths with the 124 introduction of vaccination in the early nineteenth century is very marked in both raw and 125 normalised burials. This phenomenon was observed in other cities and states that adopted 126 vaccination, and coincided with a marked decline in all-cause mortality (so the reduction in 127 normalised smallpox burials is likely to underestimate the fall in smallpox mortality). 128 We have revised the sentence in question, which now reads "The declining trend in epidemic 129 severity is temporally associated with the introduction of vaccination; unfortunately, this 130 was precisely the period over which the parish registration system collapsed, increasing the 131 difficulty of estimating the true impact of vaccination in the early vaccine era." 132 2. The term 'mortality' usually refers to mortality *rates*, that is, deaths per population at  problem, if they prefer to use normalised burials and deaths. 149 We believe that the referee has mistakenly inferred that we normalized by weekly all-cause 150 deaths. Had we done so, we would agree that this would interfere with our ability to detect 151 seasonal patterns in smallpox. Indeed, in the extreme that most deaths were attributed to 152 smallpox, dividing by all-cause deaths would remove the seasonality altogether.

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In fact, as we explain in the Normalization subsection of the Methods section, we normal-154 ized smallpox deaths by the long term trend in all-cause deaths, which has no seasonality.

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Smallpox deaths are therefore scaled conveniently without affecting seasonal patterns.  Table 1 (appendix B): the labels for the third and fourth columns appear to be transposed. 157 We have re-ordered the columns. relatively low infectivity of smallpox. 160 We have added "relatively low infectivity" to the list.  Done -thanks. We have said "waning immunity (hence a need for periodic revaccination)".  Repaired -thanks for catching these.

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Reviewer #3: 177 I appreciate the revisions that went into this manuscript, and I think it is very close to 178 publication-ready at PLoS Biology. I remain convinced that the data, by itself, is incredibly 179 valuable, and the extended analysis presented here makes this paper a more meaningful 180 contribution as well. I have only a few comments that should be straightforward to address. can learn from the statistical analysis of this data, and how will what they learn from these 185 analyses be useful, both for understanding infectious diseases more generally and also for 186 the next phase of work on smallpox specifically (e.g., building mechanistic models).

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The end of the Introduction now reads:

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Our statistical descriptions of the weekly smallpox data will help sharpen and 189 quantify research questions concerning the mechanistic origin of changes in the 190 temporal patterns of epidemics [11][12][13][14]. In addition, we present a timeline of ma- The rationale for identifying the "Intervention uptake levels" in Fig. 1 is never made clear.

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Why, for example, does the assumed uptake level go from "very low" to "low" in 1728? Why 212 does it go from "low" to "moderate" in 1740, if the first charitable variolation hospital didn't 213 open until 1746? Etc. I realize that this doesn't impact the analyses presented here (because 214 you are not seeking to draw any quantitative conclusions between the dynamics and the level 215 of intervention uptake), but I still think it would be useful to provide some justification.

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As we now clarify in the paper, we assume that the level during the period 1728-1740 was 217 between the known very low level before 1728 and the known higher level after 1740. We now 218 provide several references to support our indication of an increase to "Moderate" variolation 219 uptake levels around 1740. For example, Tucker (2002) states "variolation became popular in 220 England by the 1740s". The changes after 1768 are supported by the Razell references that 221 we cite in the main text when referring to the period of increase in popularity of variolation.

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To emphasize that we are doing the best we can with qualitative information, we now state: You do not justify the use of square-root transformation in the spectral analysis section.

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Also, in this section it would be useful to explain to a reader who has limited exposure to 228 time series analysis what is gained by carrying out both the power spectrum analysis and 229 the wavelet analysis. 230 We have expanded the introductory paragraph in the "Spectral analysis" section, which now 231 reads: 232 We used spectral analyses to identify the strongest periodicities in the smallpox 233 time series, both globally (with a traditional Fourier analysis) and locally (via 234 wavelet analysis). Before computing spectra, we normalized and square-root 235 transformed the data in order to reduce variation in amplitude without affecting 236 periodicities [74,75].

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You are missing an "of" on line 434 between "introduction" and "vaccination."

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There is some inconsistency in how Fig. 4B is discussed in the Results and Discussion. In 240 the Results, the power of the annual period is not discussed -you only mention periods at 2, 241 3, and 5 years. But in the Discussion (lines 465-466), you say that "the wavelet spectrum in 242 Fig. 4B shows a peak at one year," a finding that is not very apparent in Fig. 4B (at least 243 to me).

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Thank you. Not mentioning the one-year period in the Results was an oversight. We have 245 added the following sentence in the Results:

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A relatively weak spectral peak at one year can be seen over much of the time 247 series before 1820, though its magnitude is below the threshold for drawing a 248 black peak line except for the decade 1798-1808.

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The discussion of possible viral evolution (lines 551-559) could reference some of the theoret-  Thanks -we have now cited these papers.

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To help foreshadow the future work you anticipate in response to these data and analyses,

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You are missing an "in" on line 610 between "patterns" and "infectious." 268 Repaired -thanks for catching this.