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

Olga Krylova; David J D Earn

doi:10.1371/journal.pbio.3000506

. 2020 Dec 21;18(12):e3000506. doi: 10.1371/journal.pbio.3000506

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

Olga Krylova ^1,^¤, David J D Earn ^1,^2,^*

Editor: Andy P Dobson³

PMCID: PMC7751884 PMID: 33347440

Abstract

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.

This study presents the complete historical weekly record of smallpox mortality in London over more than 250 years (1664-1930), describes it using spectral analyses, and discusses it in the context of events and interventions that might have influenced infectious disease dynamics.

Introduction

Smallpox was declared eradicated 40 years ago, in 1980 [1], after unparalleled devastation of human populations for many centuries [2,3]. Until the 19th century, smallpox is thought to have accounted for more deaths than any other single infectious disease, even plague and cholera [2–7]. In the city of London, England alone, more than 320,000 people are recorded to have died from smallpox since 1664.

Investigation of smallpox dynamics in the past is important not only for understanding the epidemiology of a disease that has been exceptionally important in human history but also in the context of the potential for its use as a bioterrorist agent in the future [8–12]. From the historical perspective, much can be learned by relating patterns of smallpox outbreaks to demographic changes and uptake of preventative measures [13–16] and to wars and other historical events [4]. More broadly, appreciation for how intentional interventions and coincident events might impact disease dynamics is important when attempting to control the spread of any infection, including new diseases such as Coronavirus Disease 2019 (COVID-19) [17–19].

Previous work on smallpox dynamics in London has either been based on annual records [20–22] or been restricted to a few decades [23–25]. We present and examine 267 years of weekly records of smallpox mortality in London, beginning in 1664. The data span an early era before any public health practices were in place, the introduction of variolation and then vaccination, and then the decline of smallpox mortality until it became an extremely unusual cause of death. The temporal resolution in the data enables analysis of short-term fluctuations and seasonality, which are smoothed out by yearly data.

Our statistical descriptions of the weekly smallpox data will help sharpen and quantify research questions concerning the mechanistic origin of changes in the temporal patterns of epidemics [13–16]. In addition, we present a timeline of major historical events that occurred during the epoch we have studied. Overlaying the historical timeline with smallpox mortality and prevention patterns provides an illuminating view of three centuries of smallpox history.

Smallpox background

Smallpox is an acute, highly contagious, and frequently fatal disease. The name “small-pox” was first used in England at the end of the 15th century to distinguish it from syphilis, which was known as “great-pox” ([2], pp. 22–29). The disease is caused by two variants of the Variola virus, which differ substantially in severity of symptoms and case fatality proportion (CFP) ([1], pp. 1–68; [26], pp. 525–527). Variola major, which was the only known smallpox type until the beginning of the 20th century, had a CFP of 5% to 25% and occasionally higher ([1], p. 4). Variola minor (also known as alastrim), which was first recognized in 1904 [2], was less virulent and had a CFP of about 1% or less. Variola minor was the only endemic type of smallpox present in England after 1920 ([2], pp. 8, 97; [1], pp. 243). By 1935, transmission of smallpox within England appeared to have ended; further naturally acquired infections are believed to have arisen only from importation [2].

Among those who survived it, morbidity from smallpox was severe in many cases; victims could be left blind or disfigured for life [27]. In the pre-vaccination era, there were attempts to reduce morbidity and mortality from smallpox by a method initially known as inoculation, and later given the more specialized term variolation. This procedure involved deliberately infecting a healthy individual with smallpox virus taken from a pustule or dried scabs of a person suffering from smallpox [3].

Edward Jenner’s discovery of a smallpox vaccine in 1796 [28] was a major milestone, not only for smallpox control but also for modern medicine more generally, as it inspired the development of vaccines for many other pathogens. Jenner’s vaccine provided a safer, cheaper, and more effective alternative to variolation. His original method, which he called “vaccine inoculation” [28], was to inject a person with cowpox virus (Vaccinia, from the Latin vacca for cow).

The existence of a smallpox vaccine was the key factor that made eradication of the disease an achievable goal. Other important factors included the absence of asymptomatic infections, easy recognition of the disease from its symptoms, absence of an animal reservoir, and relatively low infectivity [29]. The World Health Organization launched its eradication campaign in 1967 [1,30]. Ten years later, the world’s last endemic smallpox case was registered in Somalia. In 1980, a Global Commission declared smallpox eradicated [31]. This was the first disease to be eradicated entirely by human efforts. The only remaining viral samples were stored in laboratories in Russia and the United States [11].

Data

Registration of burials in England began in 1538, when Thomas Cromwell introduced parish registers [32], but systematic summaries of deaths categorized by cause were not published until later, and only for a few towns, in Bills of Mortality. The bills reported Anglican burials, not all deaths. Later, with the creation of the office of the Registrar General in the mid-19th century, a formal system of registration of all deaths was developed and maintained.

We accessed original documents in London, England, in the Guildhall Library, the British Library, the Wellcome Library, and the London Metropolitan Archive. We digitized weekly reported birth and death records for London throughout the period over which smallpox was listed as a cause of death (1661 to 1934). The last smallpox death reported in London was in the week beginning 17 February 1934. The last year when more than one smallpox death was reported in a single week was 1930, so we do not present data or analyses after 1930 (in total, only 7 smallpox deaths were reported from 1931 to 1934).

Until 1752, the New Year was celebrated on 25 March in England [33]. However, we always indicate years following the modern practice of defining New Year’s Day to be 1 January. All data analyzed in this paper are shown in Fig 3 and are available at the International Infectious Disease Data Archive (IIDDA; http://iidda.mcmaster.ca) and at https://github.com/davidearn/London_smallpox.

Fig 3 — 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.

London Bills of Mortality

The London Bills of Mortality (LBoM) included information about baptisms and church burials, categorized by cause of death (Fig 1). The Company of Parish Clerks published the bills, based on counts collected from the individual Anglican parish registers [34,35]. Weekly bills began to be published frequently in 1604 [36], but not without long gaps until 1661. A nearly continuous weekly sequence of bills survives starting 18 October 1664.

The accuracy of the LBoM has been considered by a number of historians and demographers [23,37–42]. Shortcomings that are often highlighted include:

Omissions. Only burials within Anglican grounds were included; Roman Catholics, Jews, Quakers, and other nonconformists were excluded [39–42].
Geographical coverage. The LBoM did not include some fast-growing parishes and did not reflect expansion of London’s boundaries due to population growth [40,42].
Accuracy of parish returns. Parish returns were sometimes missing or inaccurate [40,42,43].
Exported burials. Some Londoners were buried outside the city boundaries [23,40,41].
Declining accuracy. After 1790, an increasing number of poor Londoners were buried in non-Anglican grounds and were not registered [39].
Unsubmitted returns. Beginning around 1830, some parishes stopped submitting their returns [43]. (In Fig 3, we annotate the period from 1790 to 1841 as a “Progressive collapse of the parish registration system”.)

All of these data quality issues led to underreporting of mortality. Nevertheless, the data from the LBoM are “probably more complete and more accurate than any available elsewhere in England in that time” [37] and remain the most comprehensive summaries of baptisms and burials of the 17th and 18th centuries in London.

While the bills are certainly not a perfect record of mortality, it is reasonable to assume—as we do in this paper—that the temporal pattern of smallpox burials quantified in the LBoM, is roughly proportional to the true historical smallpox mortality in London. We implicitly assume that changes in the degree of underreporting of smallpox deaths were sufficiently slow that we can make inferences about seasonality of smallpox deaths and the frequency of epidemics. However, from the LBoM, we can estimate only a lower bound for the total burden of smallpox deaths in London between 1661 and 1841.

Reporting of smallpox deaths

Burials are tabulated by cause in the LBoM, but the Bills predated formal classifications of disease, casting doubt on the reliability of the listed causes [37,40,44]. However, smallpox records are likely among the most accurate in the LBoM, due to the unique and easily identifiable presentation of the disease ([36], p. 530; [37,40,43]).

Before 1701, smallpox was listed in the weekly LBoM under the heading “flox and smallpox”. “Flox” is an older term that referred to a rare type of smallpox infection involving especially severe symptoms, including hemorrhaging, and high case fatality (approximately 96%) ([36], p. 436). After 1701, “smallpox” was used consistently. Other disease names that occur in the bills and are considered by some to be associated with smallpox are “flux” and “bloody flux”. Razzell [3] suggested that bloody flux was a name used for hemorrhagic smallpox and that it was considered a distinct disease ([3], p.104). However, Creighton [36] described bloody flux as an old name for dysentery and not as something related to smallpox ([36], p.774). Other historians also refer to “bloody flux” and “flux” as diseases not related to smallpox, but rather the names for dysentery and diarrhea respectively ([45], p. 401; [46], p. 45; [47], p. 611). In any case, mortality from “bloody flux” and “flux” was negligible compared to smallpox (<5,000 deaths in total from “bloody flux” and “flux” compared to 322,219 total smallpox deaths).

Consequently, even if they were truly smallpox deaths, including them would not significantly influence our findings. We therefore used the sum of “flox and smallpox” and “smallpox” records and did not include “bloody flux” and “flux” in our data.

Transition to the Registrar General’s Weekly Returns

By the end of the 18th century, it was evident that a better system of collection of vital statistics was needed in England. The accuracy of the old system of parish records had been compromised by the rapid growth of London’s population [48]. The Registrar General’s Office was created in 1836 by the Births and Deaths Registration Act [49] to provide a comprehensive and accurate national registration system of births, marriages, and deaths, including causes of death ([50], p. 77).

The new (national) system of civil registration began in 1837, and the first Registrar General’s Weekly Return (RGWR) was published for the week ending 11 January 1840 ([51], p. 119). Unlike the LBoM, the new registration system included all deaths (not only burials), all sectors of the population (not only Anglicans), and greater geographical coverage. Initially, five additional parishes were included [39]. Other areas were added when the RGWRs were established, and this expanded area was used to define the metropolis in the 1841 census [52]. A thorough review of the quality of data in the Registrar General’s Returns is provided by Hardy [44].

In 1841, 234 smallpox deaths were reported in the LBoM. In 1842, only 34 smallpox deaths were reported in the LBoM, whereas 357 were reported in the RGWR. We use the RGWR from January 1842 onwards.

Heaping during the transition period

From the middle of the 18th century, there was often a week late in the year with a remarkably high number of deaths reported in the LBoM. This phenomenon is well known ([53], p.14) and resulted from backlogged records being submitted together (heaped), typically in early December in the last reporting week of the year.

To address the problem of heaping, we examined each year from 1760 to 1841 and performed the following steps:

We considered the number of reported smallpox deaths from week 45 of the focal year to week 5 of the next year.
We classified as a heap week any week from week 45 to week 5 in which reported smallpox mortality was more than three standard deviations from the median of these weeks.
We verified by visual inspection that the automatically detected heap weeks were indeed unusual, and we looked for visually apparent heap weeks that were missed.
We replaced the reported smallpox deaths in heap weeks with the average of the previous and following weeks.
We calculated the difference between original heaped count and the replaced value (the excess due to heaping) and redistributed this number of smallpox deaths in proportion to reported smallpox throughout the year (so the adjusted counts have noninteger values). This redistribution ensured that the original and revised time series contained the same annual numbers of smallpox deaths. (We separately considered redistributing the excess uniformly throughout the year and did not detect any differences in our results.)

The first year with a heap week identified in this way was 1768, and the last was 1841. Thirty-nine years with heap weeks were discovered by the three standard deviations criterion. Another 14 years with heap weeks were identified visually, giving a total 51 years involving heaping. From 1793 to 1841, almost every year had a heap week.

Missing weeks

The mortality bills for some weeks have been lost. Fortunately, all gaps are small (typically 1 to 5 weeks) with the largest gap being 9 weeks. We filled all gaps using linear interpolation, so there are no missing values in the final time series.

Consistency checks

Annual summaries of mortality were published in London from 1629 onwards. Initially, these were annual Bills of Mortality, and later, they were annual summaries of the Registrar General’s Returns. Creighton [36] tabulated annual smallpox mortality in London for the period 1629 to 1893 (based on annual Bills of Mortality until 1836 and on the Registrar General’s Annual Returns for 1837 to 1893). In Fig 2, we compare these annual counts with annual aggregations of our weekly data.

Fig 2 — 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.

Differences between the two data sets are indicated with white stacked bars if the annual counts from Creighton are larger, and black stacked bars if our annual sums from the weekly data in this paper are larger. Before 1664, there are no weekly data, so the bars are entirely white. After 1893, we show only our annual sums and color them red.

Annual smallpox mortality was greatest in 1871; our annual sum for that year is 7,982, and Creighton’s table indicates 7,912. The top of this bar is cut off in Fig 2. In all other years, there were fewer than 4,000 smallpox deaths.

The data from the two sources align well for most years. The most substantial discrepancies are during the period of transition from the Bills of Mortality to the Registrar General’s Returns (1837 to 1841); we summed weekly LBoM data for this period, whereas Creighton used the Annual Registrar General’s Returns. Creighton notes that the annual count for 1837 includes only six months, not the full year ([36], p. 613), but even so, it exceeds our sum from the weekly bills (which is not surprising given the much larger geographical area covered by the Registrar General’s Returns; see Transition to the Registrar General’s Weekly Returns section).

London’s population

Decennial censuses of London began in 1801 [54]. We estimated London’s population at earlier times based on Finlay and Shearer [55] for the period up to 1700, and Landers [40], who provides decadal population estimates from 1735 to 1795 (see Table 1 and the top of Fig 3).

Table 1. Population of London, England (1550–1931).

Year	Inner London	Outer London	Total London	Source
1550	120,000		120,000	[55]
1560	140,800		140,800	[55]*
1580	180,400		180,400	[55]*
1600	200,000		200,000	[55]
1620	297,000		297,000	[55]*
1640	390,500		390,500	[55]*
1650	391,450		391,450	[55]*
1660	392,400		392,400	[55]*
1680	468,600		468,600	[55]*
1700	490,000		490,000	[55]
1735	660,000		660,000	[40]
1745	670,000		670,000	[40]
1750	675,000		675,000	[55]
1755	680,000		680,000	[40]
1765	730,000		730,000	[40]
1775	780,000		780,000	[40]
1785	826,502		859,234	[40]
1795	909,507		1,007,703	[40]
1801	959,310	137,474	1,096,784	[54]
1811	1,139,355	164,209	1,303,564	[54]
1821	1,379,543	193,667	1,573,210	[54]
1831	1,655,582	222,647	1,878,229	[54]
1841	1,949,277	258,376	2,207,653	[54]
1851	2,363,341	288,598	2,651,939	[54]
1861	2,808,494	379,991	3,188,485	[54]
1871	3,261,396	579,199	3,840,595	[54]
1881	3,830,297	883,144	4,713,441	[54]
1891	4,227,954	1,344,014	5,571,968	[54]
1901	4,536,267	1,970,622	6,506,889	[54]
1911	4,521,685	2,638,756	7,160,441	[54]
1921	4,484,523	2,902,232	7,386,755	[54]
1931	4,397,003	3,713,355	8,110,358	[54]

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Entries with an asterisk were estimated based on linear interpolation from ([55], Tables 2 and 5).

Finlay and Shearer [55] estimated the total population of London for every half century from 1500 until 1700 based on information about the population north and south of the river Thames, taking into account inaccuracies in data collection. Their book [55] also contains data for other years for the population north ([55], Table 2) and south [55] of the river that were not included in their summary ([55], Table 5). Population numbers for some years, for the south of the river, were missing (years highlighted with an asterisk in Table 1); we used linear interpolation to estimate the population south of the river for these missing years. Final total population estimates were calculated by the same method as in [55], i.e., adding the populations north and south of the river and multiplying the sum by an inflation factor (1.1, except 1.2 in 1650 and 1660) to account for inaccuracy in data reporting. Note that Finlay and Shearer’s estimate for 1650 appears to be inaccurate due to an arithmetic error (according to their own figures, it should be approximately 400,000, not 375,000).

Annotation of data with historical events

Over the 267 years that we study, London underwent major demographic and social changes, and there were a variety of historical events that may have had substantial impacts on smallpox dynamics. The introduction of smallpox control measures (variolation and later vaccination) would be expected to influence smallpox dynamics. Other events that could potentially have impacted smallpox epidemics include wars [56,57] and the Industrial Revolution, which was accompanied by urbanization and demographic transitions [58–61]. We annotate the smallpox time series in Fig 3 with the major events and developments that we describe below.

Control-free era

The first recorded outbreak of smallpox in England is dated to 12 August 1610 ([36], p. 435). The first annual Bill of Mortality (1629) recorded only 72 burials due to smallpox, but later, bills often listed many more; in 1634, for example, the annual Bill recorded 1,354 smallpox burials ([36], p. 436). The cumulative death toll from smallpox over the course of the 17th century eventually exceeded plague, leprosy, and syphilis [2,35,40]. According to the annual Bills of Mortality, there were approximately 97,000 burials due to smallpox between 1629 and 1721 (excluding 1637 to 1646, for which there are no extant mortality bills) [36].

Early variolation, 1721 to 1740

Lady Mary Wortley Montagu (an influential writer and poet [62]) is credited with introducing variolation to Great Britain [1–3,30,63]. She had her daughter professionally variolated in London in April 1721 (this year is annotated with “Introduction of variolation” in Fig 3). For the next two decades, variolation occurred but was not popular. Only 857 people were variolated in the whole of Great Britain from 1721 to 1727 and only 37 in 1728 [36]. The variolation level for this period is consequently indicated as “Very low” in Fig 3. In the decade following 1728, the frequency of variolation is unknown, but we assume it was between the very low level before 1728 and the moderate level later when it became a more common practice (in Fig 3, the period 1728 to 1740 is indicated as “Low” variolation levels). English medical practitioners implemented variolation very crudely with deep incisions that caused severe symptoms, morbidity, and high mortality of up to 2% ([64], p. 464) [65].

Increasingly common variolation, 1740 to 1808

Variolation became more popular in the 1740s (indicated by “Moderate” uptake levels in Fig 3) ([64], p. 466; [66], p. 4; [67], p. 17; [68], p. 18). Initially, only the rich could afford it, but charitable variolation began with the establishment of the London Smallpox and Inoculation Hospital in 1746 (annotated in Fig 3).

Until 1762, variolation was usually preceded by four to six weeks of preparation, which included purging, bleeding, and a restricted diet with limited quantities of food. Variolation was followed by an isolation period of two or more weeks. Isolated individuals were placed in purpose-built inoculation houses ([1], [3], p. 255). The preparation period was shortened after Robert Sutton’s improvement of variolation using light incisions in 1762 (annotated in Fig 3). Sutton’s new method dramatically decreased the severity of symptoms and death and reduced the cost. Consequently, it became more common to offer variolation to the poor population free of charge.

Sutton’s variolation technique spread quickly around England and became very popular in rural areas. When a new epidemic appeared to be highly probable, “general variolation” of entire villages and communities was performed. In large towns and cities, the situation was quite different [25]. In London, the use of variolation was irregular and attempts to perform “general variolation” were sporadic and rare.

Poor Londoners were variolated only through Smallpox Charities. They performed public variolation in batches, separately for males and females, 8 to 12 times a year ([36], p. 506). The charities did not admit children under 7 years of age despite the fact that the vast majority of smallpox cases at that time were in infants and young children ([36], p. 507).

The full extent of variolation in London after the Suttonian innovation is unclear. The figures from London Hospital show that the number of variolated individuals increased dramatically from 29 in 1750, to 653 in 1767, and 1084 in 1768 ([36], p. 506). Based on a variety of historical reports, Razzel concluded that variolation gained considerable popularity in London at the turn of the 19th century ([3], p. 72). From these qualitative descriptions, it seems likely that uptake of variolation increased after 1768 and reached a maximum during 1790 to 1808 [3,69] (annotated in Fig 3).

Industrial revolution

During the Industrial Revolution (annotated as 1760 to 1830 [70] in Fig 3), a “growing number of people moved to urban centres” [71] such as London, precipitating significant demographic and social changes [38,58–61]. London’s population more than doubled from about 730,000 in 1765 to about 1,900,000 in 1831 (see Table 1 and section on London’s population). If this increase in population size was associated with an increase in population density, and/or an increase in the average number of contacts people had, then the rate of transmission of smallpox would have increased and affected epidemic patterns [72]. Transmission dynamics would also have been affected by changes in fertility [13,15], which may [38,60] or may not [58] have increased during the Industrial Revolution. It has also been proposed that smallpox transmission increased as a result of viral evolution during this period [23–25].

Vaccination

The idea of vaccination was initially met with skepticism by the scientific and medical communities [1,2]. Jenner “was advised not to send a record of his observations to the Royal Society, which was prepared to refuse it, but to publish it as a pamphlet; and as a pamphlet it appeared in 1798” ([73], p. 62).

Unlike variolation, vaccination came with relatively little risk to the vaccinee, no preparatory period, and much lower cost. Consequently, in spite of the initial skepticism, vaccination was adopted by the public more quickly and more widely than variolation ever was [1]. There were initially many impediments associated with ineffective vaccine distribution and storage, shortage of cowpox virus, inadequate vaccine efficacy, waning immunity (hence a need for periodic revaccination), and religious and philosophical objections. These challenges were overcome over the course of the 19th century, and by the turn of the 20th century, vaccine uptake had risen sufficiently to cause a dramatic decline in smallpox mortality (Fig 3).

Unfortunately, quantitative reports of early smallpox vaccine uptake are sorely lacking. Vaccinations were poorly recorded until the end of the 19th century. Available data are incomplete, uncertain, and inconsistent. For example, the figures from the London Smallpox and Inoculation Hospital show the percentage of vaccinated patients admitted to the hospital increasing steadily from 32% in 1825 to 73% in 1856 [74], whereas the Royal Commission on Vaccination found that only 25% of newborns were vaccinated by 1820 and about 70% in some parishes by 1840 [35]. Mooney [75] states that during 1854 to 1856, the percentage of vaccinated infants might have ranged from 28% to 81% based on one source, but that another source indicates that infant vaccination rates for London during the period 1845 to 1890 were much lower than the national average and never increased above 500 per 1,000 live births (i.e., 50%). There appear to be no surviving records concerning vaccinations of older age groups during this period; however, it is hypothesized that many adults escaped vaccination ([74], p. 117). In Fig 3, we indicate the qualitative pattern of change in vaccine uptake.

Better access and increasingly strong legislation concerning vaccination

A number of additional developments and policy changes during the 19th century are indicated in the timeline in Fig 3.

State involvement in the control of smallpox in England began with the foundation of the National Vaccine Establishment in 1808. It provided free vaccination at its London stations and distributed vaccine to other parts of England [76]. Around this time, the London Smallpox and Inoculation Hospital ceased variolation and began vaccination in greater numbers. Smallpox outbreaks over the next decade were very mild, possibly resulting from increased vaccination; however, this was precisely the period of the Napoleonic Wars (1803 to 1815) during which other infectious diseases were also less prevalent than usual in England ([36], p. 569).

A strikingly large smallpox epidemic occurred in London from 1837 to 1838 and exploded into a European wide pandemic [2]. The authorities in England realized that some radical measures had to be taken, which led to the first Vaccination Act of 1840, providing vaccination free of charge and banning variolation. It was followed by the Vaccination Act of 1853, which made vaccination of every child during the first four months of life compulsory. The Vaccination Act of 1867 introduced penalties for not complying with compulsory vaccination.

The Franco–Prussian war, which began in late July 1870, is believed to have initiated the worst pandemic of smallpox in all of Europe in the 19th century. It resulted in at least 500,000 deaths. England alone lost more than 40,000 people. Thanks to compulsory vaccination, fatality rates in England were three times lower than in Prussia, Austria, and Belgium ([2], pp. 87–91). The immediate response of the English government to this devastating pandemic was the Vaccination Act of 1871, which enforced very strict control (through the courts) of the implementation of the previous Acts.

In the second half of the 19th century, many vaccine-related challenges were resolved. Arm-to-arm vaccination (vaccine transfer from the infectious pustule of vaccinated individual to a nonvaccinated individual [1]) was the main method of vaccine distribution in the beginning of the century. It was dangerous because it could transmit other diseases such as syphilis and was consequently outlawed in 1898 [2]. It was replaced by the new technique of passing cowpox from cow to cow. The new method of vaccine distribution was first introduced in Naples, Italy, in 1843 [77,78]. However, it arrived in England only in 1881. Another important discovery was made in 1891 by Monckton Copeman [78], who demonstrated that adding glycerine to smallpox vaccine reduces bacterial contamination, making it more efficacious and reliable.

Eradication in the 20th century

The last large outbreak of Variola major occurred in London from 1901 to 1902 (Fig 3) and was probably seeded from another country [74]. After 1902, only very small outbreaks occurred with very low incidence and very few deaths.

In 1967, the World Health Organization launched its global smallpox eradication campaign. In 1980, smallpox was certified as the first infectious disease to be eradicated by human efforts [27].

Methods

We used a variety of methods to elucidate the patterns in the London smallpox time series. Spectral analyses and a visualization of seasonality allow us to reveal important characteristics of the data that cannot be gleaned by inspection of the raw time plot (Fig 3).

Normalization

Due to population growth and changes in city boundaries, the size of the population from which smallpox deaths were reported for London changed over the course of the time series. In addition, sampling of deaths in the LBoM was less complete in the last few decades before the establishment of the RGWR. Sampling deficiencies presumably affected deaths from all causes in the same way; consequently, we attempted to obtain a consistent normalization of weekly smallpox deaths by dividing by the trend of weekly all-cause mortality (ACM) in London, rather than estimated population size. To calculate the trend in ACM, we used Empirical Mode Decomposition (EMD), which is designed to identify trends in nonlinear and highly nonstationary time series [79,80,81]. EMD was developed to overcome the drawbacks of moving averages, other linear filters, or linear regression, which often perform poorly on nonstationary data. EMD decomposes a signal into several components with a well-defined instantaneous frequency via intrinsic mode functions (IMFs). IMFs are basically zero-mean oscillation modes present in the data: The first IMF captures the high frequency (shorter period) oscillations, while all subsequent IMFs have lower average frequency (longer period). Each IMF is extracted recursively starting from the original time series until there are no more oscillations in the residue. The last residual component of this process can be considered an estimate of the trend [80].

Spectral analysis

We used spectral analyses to identify the strongest periodicities in the smallpox time series, both globally (with a traditional Fourier analysis) and locally (via wavelet analysis). Before computing spectra, we normalized, square-root transformed, and detrended the data in order to reduce variation in amplitude without affecting periodicities [82,83].

Classical power spectrum

We computed the standard power spectral density [14,84–86] of the entire smallpox time series to obtain a global estimate of its frequency content. We used the R [87] function spec.pgram with no taper (taper = 0) and a standard modified Daniell smoother (kernel = kernel("modified.daniell",c(3,3))).

Wavelet spectrum

Because infectious disease time series are typically highly nonstationary, wavelet analysis has become increasingly popular in epidemiological research [16,82,83,88–90]. We computed a wavelet transform [91,92] of the smallpox time series in order to examine how smallpox periodicities changed over the course of the three centuries.

A wavelet transform is computed with respect to a basic shape function, the analyzing wavelet, which has a scale parameter that controls its width. Narrower (wider) scales correspond to higher (lower) frequency modes in the time series. At any given time and scale, a stronger correlation between the analyzing wavelet and the signal yields a larger value of the wavelet transform. We obtain a complete (two-dimensional) time-frequency representation of the data by convolving the analyzing wavelet—at each scale—with the original time series. We used the Morlet wavelet [92] as the analyzing wavelet to obtain the wavelet transform of the smallpox time series.

The standard computation of the wavelet spectrum requires that the number of points in the time series be a power of 2. Consequently, we pad the ends of the time series with zeros to bring the number of time points in the data to the nearest power of 2. The resulting artificial discontinuity where the zero-padding begins reduces the accuracy of the wavelet transform at the ends of the time series. Regions of lower accuracy are identified by the cone of influence. Data outside this cone should be interpreted with caution. Ninety-five percent confidence regions are computed based on 1,000 Markov bootstrapped time series [83,89].

Seasonality

An indication of underlying seasonality in a time series is the occurrence of a spectral peak at a period of one year. However, this crude measure suppresses the detailed seasonal pattern and, in particular, does not reveal the times of year when peaks or troughs occur.

Following Tien and colleagues [7], we visualized the evolving seasonal pattern of smallpox dynamics with a heat map in the time-of-year versus year plane (we refer to this as a seasonal heat map).

Before constructing the seasonal heat map, we square-root transform and detrend the normalized smallpox time series (because we have found that seasonality is represented mostly clearly after this transformation). Detrending has the effect of shifting the local mean at a given time toward the global mean of the entire time series. Consequently, the last few decades of the smallpox time series, which have a true mean close to zero, are represented by “medium heat” in the seasonal heat map because the true zeros are shifted to the global mean.

To further clarify changes in smallpox seasonality, we separately identified the peak week of each epidemic by visual inspection of the normalized time series, and displayed all peak weeks in the time-of-year versus year plane. To assist with identification of trends, we also computed a moving average of the week-of-the-year in which an epidemic peak occurred (using a circular average that considered week 53 and week 1 to be the same). Our moving average was calculated with a 21-epidemic window, i.e., each plotted point is the average of the previous 10, current, and next 10 epidemic peak weeks (peaks did not necessarily occur every year).

Results

Patterns in the raw time series

The time plot of the raw data (Fig 3, top panel) displays substantial changes in the structure, amplitude, and frequency of smallpox epidemics over time. However, some of the apparent changes are misleading because they do not account for population growth and inconsistency of data sources. For example, the epidemic of 1871 appears to be the largest, but it was not the largest relative to population size or relative to ACM. In contrast, the epidemic of 1838, which is frequently mentioned in the literature [2,36], is not easily identifiable in the raw data, likely because it occurred just at the time of transition between the LBoM and the RGWR.

Normalization

Weekly ACM in London (1661 to 1930) and the EMD-computed trends for the periods 1661 to 1841 and 1842 to 1930 are presented in Fig 4. The large difference in population coverage (see Data section) between the LBoM and RGWR is evident.

Patterns in the normalized time series

The bottom panel of Fig 3 shows the weekly London smallpox time series normalized by the ACM trend.

The raw and normalized time series emphasize different features of smallpox dynamics in London. For example, in the bottom panel of Fig 3, the epidemic of 1838 is easily identifiable, and the epidemic of 1871 is much less extreme in magnitude compared with other epidemics of the 19th century.

From the earliest times in the series, there were recurrent epidemics. Four large outbreaks in 1667, 1674, 1681, and 1694 stand out in the normalized time series, and an epidemic of this magnitude did not occur again until 1752. The epidemic pattern before about 1705 appears to have been less stationary than the pattern in the subsequent decades (the frequency and amplitude of outbreaks was more consistent from 1705 to 1750).

The years from 1770 to 1810 were characterized by stricter regularity of epidemics. This period coincided with more common variolation (the practice gained popularity after the Suttonian innovation of 1768). Beginning around 1810, the data show a dramatic reduction in the amplitude of epidemics, though outbreaks were more frequent and the data are noisier. The declining trend in epidemic severity is temporally associated with the introduction of vaccination; unfortunately, this was precisely the period over which the parish registration system collapsed, increasing the difficulty of estimating the true impact of vaccination in the early vaccine era.

After 1835, interepidemic intervals increased and (normalized) epidemic peak heights declined, with the exception of four large epidemics in 1837, 1871, 1876, and 1902. During this period, variolation was eliminated and vaccination levels increased. The coincidence of the 1840 Vaccination Act (which made variolation illegal) with the radical change in data collection from the LBoM to the RGWR limits our ability to identify potential causal links between policy and behavioral changes and epidemic patterns.

The bottom panel of Fig 3 also shows the EMD-computed trend of normalized smallpox mortality in London over the centuries. As a proportion of ACM, smallpox mortality rose steadily from 1664 until 1680 and then fell until about 1700. After this drop, the trend generally increased (with a shallow dip around 1740) until approximately 1770. After 1770, the trend declined gradually until 1908, when smallpox deaths were nearly eliminated in London.

After 1840, epidemics became more regular with a longer interepidemic period of 3 to 4 years. After the exceptionally large epidemic of 1871 (there were 10,618 reported smallpox deaths from 1 January 1870 to 31 December 1872), subsequent smallpox outbreaks were much smaller and irregular. The last substantial outbreak was in 1902, after which there were very few smallpox deaths reported.

Spectral analysis

Classical power spectrum

Fig 5 shows the period periodogram (power spectrum as a function of period) for the full smallpox time series. A strong peak at one year suggests underlying seasonality of epidemics. Other peaks (near 2.2, 2.4, 3, 5.1, and 6 years) suggest more complex dynamical patterns.

Wavelet spectrum

Fig 6B shows the wavelet transform of the normalized London smallpox time series. Colors indicate the strength of signal at given periods (blue meaning weak and red meaning strong). The cone of influence and 95% confidence contours are shown in black.

The black curves through the bright areas of Fig 6B indicate the periods with greatest power at each time point. From 1664 to about 1720, multiple spectral modes are prominent (initially periods near 2, 3, and 5 years, then near 3 and 5 years only from 1690 to about 1705, and then near 2 years only until about 1728). There is a weak signal between 2 and 3 years from 1728 to 1740, and then a strong signal near 2 years (1740 to about 1765) and near 3 years (about 1770 to 1808). A relatively weak spectral peak at one year can be seen over much of the time series before 1820, though its magnitude is below the threshold for drawing a black peak line except for the decade from 1798 to 1808.

From about 1808 to about 1832, the time series is markedly noisier, displays much lower amplitude fluctuations, and much weaker spectral signals. The decay of the parish registration system may have contributed to this temporal pattern, though the clear recurrent epidemic pattern that emerges about 1832—well before the beginning of the RGWR era—suggests that there were genuine changes in smallpox dynamics at the end of the LBoM era, not just a change in sampling.

Seasonality

Fig 6C shows the seasonal heat map for smallpox mortality in London, and Fig 6D shows all peak weeks in gray and the moving average peak week (computed from the 21 nearest outbreaks) in red. The seasons are indicated approximately with horizontal dashed lines: Winter (week 1, the first week of January), Spring (week 13, end of March), Summer (week 26, end of June), and Fall (week 39, end of September).

Reported smallpox mortality was lowest in the spring until about 1840, and in the fall/winter afterwards (these are the bluest regions in Fig 6C). The time series is generally very noisy during the troughs between epidemics, and there is rarely a clear minimum week.

Around 1750, there was a shift in the typical timing of outbreak peaks from summer/fall to fall/winter. This change is clearest in the red moving average in Fig 6D. Epidemic patterns might have become less seasonal during the period from 1808 to 1840 (the range of “temperature” is narrower in the heat map in this segment of Fig 6C). After 1840, as epidemics became less frequent, they peaked in the winter/spring.

Discussion

We have digitized and analyzed what is, to our knowledge, the longest existing weekly time series of infectious disease mortality. The time span of the data, from 1664 to 1930, covers an extraordinary period in London, England, during which smallpox changed from a terrifying and unavoidable danger to an easily preventable infection.

Previous work on smallpox dynamics in London

A number of previous studies of smallpox in London are complementary to the analysis presented here.

In the 1990s, Duncan and colleagues [21,93,94] studied annual smallpox mortality in London, from 1647 to 1893, and estimated interepidemic intervals in five segments of the time series ([21], Table 1) (these results are reproduced in Fig 7). These authors attributed changes in interepidemic intervals to population growth, malnutrition associated with changes in wheat prices, and seasonal variations in temperature and humidity. Cliff and colleagues ([48], p. 101) have also estimated interepidemic intervals for smallpox in London using traditional time series analysis (also reproduced in Fig 7). For comparison, in the lower panel of Fig 7, we show the interepidemic intervals inferred directly from the time between adjacent peaks in the smallpox time series.

Fig 7 — 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.

More recently, Davenport and colleagues [23–25] have examined individual, age-specific death records in a large area of London over a period of several decades (1752 to 1805). These authors discovered that, after 1770, smallpox mortality declined in adults and rose in children. They suggested that this change in the age distribution of smallpox mortality might have been a consequence of evolution of increased transmissibility of the Variola virus.

New data and descriptive statistics

Digitization of the full weekly record of mortality from smallpox (and from all causes) in London has enabled us to conduct a number of informative analyses that reveal changes in the seasonal structure of smallpox epidemics over the centuries. The wavelet spectrum (Fig 6B) provides a more detailed view of the periodic structure of smallpox than has been accessible previously. In addition, our seasonal heat map (Fig 6C) and epidemic peak time visualization (Fig 6D) show how the seasonal timing of outbreaks varied over many decades.

The annual data that have been studied previously smooth out the seasonal patterns that we have identified and restrict the resolution of spectral features. Even the classical power spectrum of the weekly data (Fig 5) reveals noninteger periods that cannot be detected from annual counts, and the wavelet spectrum (Fig 6B) shows gradual changes in periodic structure. In Fig 7, we compare the spectral peaks from our wavelet spectrum with the interepidemic intervals previously estimated from annual data.

Interpretations

The primary role of vaccination in the ultimate elimination of smallpox mortality in London is not in question. However, the causes of the various transitions in the spectral and seasonal structure of smallpox dynamics over the decades and centuries are not clear.

The historical timelines of events and uptake of interventions, shown alongside the smallpox data and analyses in Fig 3, should aid in formulating mechanistic hypotheses, especially in relation to the history of control strategies. Previous work has shown that long-term changes in birth rates and vaccination levels have induced transitions in transmission dynamics of other infectious diseases [13–16]. Time series of additional historical and environmental variables are also important to consider. Economic factors, such as wheat prices [21], might have affected transmission and/or mortality rates. Weather changes, especially in humidity and temperature, may also have influenced seasonality of smallpox [21,40], and climatic changes (see Fig 1 of [95]) could have influenced periodic dynamical structure over longer timescales.

More information about the age, social, and spatial structures of smallpox mortality would be extremely valuable. A case in point is the discovery by Davenport and colleagues [23–25] that, around 1770, smallpox burials declined in adults and rose in the very young. This shift in age structure of mortality seems likely to have been driven by a corresponding shift in the age structure of infections. The most obvious potential cause of a trend toward younger age at infection is an increase in the transmission rate [72]. Davenport and colleagues suggest that greater transmission may have resulted from “a sudden increase in infectiousness of the smallpox virus” ([23], p. 1289). Alternatively, the virus could have evolved to yield a longer infectious period.

The plausibility of unusual viral evolution around 1770 is supported by recent molecular genetic analyses, which found that “diversification of major viral lineages only [occurred] within the 18th and 19th centuries, concomitant with the development of modern vaccination” [96]. It is certainly possible that evolutionary pressures resulting from changes in control strategies could have selected for increased transmission [97,98]. Of course, a variety of other factors could also have contributed to a rise in the transmission rate. In particular, more common variolation could have promoted transmission (even if it reduced mortality), and population density might have risen during the Industrial Revolution, as mentioned above.

Seasonality

Any or all of the sociodemographic, behavioral, and environmental factors mentioned above might have contributed in some way to the dramatic changes in the time of year when smallpox mortality peaked over the centuries (Fig 6C and 6D). Recurrence of outbreaks does not necessarily imply that transmission dynamics are seasonally driven. However, the wavelet spectrum in Fig 6B shows a peak at one year from the beginning of the time series until the early 19th century, and the strong spectral peak at exactly one year in Fig 5 suggests underlying exogenous forcing by strictly seasonal variables (e.g., weather, holidays, or migrations during harvests).

If smallpox transmission was seasonally forced, then the implications for dynamical interpretations of the time series are significant. Seasonal forcing of infectious disease transmission can stimulate persistence of complex epidemic cycles [99] and chaos [100]. The mechanistic origin of seasonal forcing may [101] or may not [102] be easy to determine. In the case of smallpox, previous work [1,23,103] found that, in temperate climates, the majority of smallpox cases occurred in the winter and spring, whereas in tropical climates, the seasonality was less pronounced. The general conclusion was that smallpox incidence always increases when the weather is cool and dry; this belief influenced the planning of the eradication campaign in India and seemed to help to improve its efficiency [1]. Previous smallpox seasonality studies were mainly based on data from the 19th and the 20th centuries, when preventative measures were already common [1,103]. Our data set is of a particular interest in this respect since it includes a period when only naturally acquired smallpox immunity existed.

Explaining transitions in smallpox dynamics

Our goal in this paper has been to describe—and make publicly available—the weekly time series of smallpox mortality in London, and to present information on a variety of historical factors that might have influenced smallpox dynamics over the centuries. The annotated data (Fig 3) will help to frame hypotheses about the mechanisms that were responsible for the observed smallpox mortality patterns, including transitions from one type of pattern to another. Our spectral and seasonal analyses (Figs 5–7) quantify transitions in smallpox dynamics that should be possible to explain using mechanistic mathematical models [72,86,104,105].

Dynamical transitions in measles [13,16] and other childhood infections [14] during the 20th century have been successfully explained with mechanistic models, using observed changes in susceptible recruitment (through changing birth rates and vaccination levels) to predict changes in the frequency structure of epidemic patterns [13–16,86]. For historical smallpox in London, we do have relevant birth data (shown in the top panel of Fig 3), but only qualitative information about vaccination levels (and earlier variolation levels, the effects of which are not entirely clear). Moreover, the time series is so long that the underlying pattern of seasonal forcing probably changed substantially. Changes in seasonal forcing can be accommodated in predictions [16,106], and estimation of underlying seasonal variation in transmission is becoming easier [107]; however, obtaining a convincing mechanistic explanation for all the structure we have identified in London’s smallpox dynamics represents a major challenge.

Ultimately, we anticipate that meeting this challenge will involve further developments of the existing theory of transitions in epidemic patterns [13–16,106], coupled with state-of-the-art methods of inference to obtain parameter estimates for dynamical models [108–112].

Conclusions

“The greatest killer” [2] has not circulated since its eradication in 1980. While smallpox research in recent years has understandably tended to focus on the potential for accidental or intentional reintroduction in the future, it is enlightening to look back in time. The long history of documenting smallpox mortality in London provides an extraordinary opportunity to learn from the past about changing patterns in infectious disease transmission.

Much remains to be understood about the data we have presented in this paper. From an ecological perspective, the key challenges are to explain the observed smallpox dynamics in London as consequences of intrinsic nonlinear interactions, influenced by identifiable extrinsic forces.

Better control naturally led to less smallpox mortality over time. However, how interventions influence the frequency structure and seasonality of epidemic time series over decades and centuries is much more subtle [13–15]. While preliminary work has been promising [113], careful estimation [114,107] and analysis [15,106] of patterns of seasonal forcing will be required in order to use mechanistic models reliably to explain [16] the observed transitions in smallpox transmission dynamics.

Acknowledgments

The data were photographed and/or entered primarily by Kelly Hancock, Claire Lees, James McDonald, Laxmi Pandit, and David Richardson. Valerie Hart facilitated work at the Guildhall Library, City of London. Bernard Cazelles shared his code for computing wavelet spectra. We thank all members of the Mathematical Biology Group at McMaster University for helpful comments and discussions.

Abbreviations

ACM: all-cause mortality
CFP: case fatality proportion
COVID-19: Coronavirus Disease 2019
EMD: Empirical Mode Decomposition
IIDDA: International Infectious Disease Data Archive
IMF: intrinsic mode function
LBoM: London Bills of Mortality
RGWR: Registrar General’s Weekly Return

Data Availability

All data are available at https://github.com/davidearn/London_smallpox and at the International Infectious Disease Data Archive at http://iidda.mcmaster.ca.

Funding Statement

Natural Sciences and Engineering Research Council of Canada (NSERC, http://www.nserc-crsng.gc.ca). NSERC Discovery Grant to DE. NSERC Postgraduate Scholarship to OK. J. S. McDonnell Foundation (JSMF, http://jsmf.org) Research Grant to DE. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS Biol. doi: 10.1371/journal.pbio.3000506.r001

Decision Letter 0

Roland G Roberts

9 Sep 2019

Dear Dr Earn,

Thank you for submitting your manuscript entitled "Patterns of smallpox mortality in London, England, over three centuries" for consideration as a Research Article by PLOS Biology.

Your manuscript has now been evaluated by the PLOS Biology editorial staff, as well as by an academic editor with relevant expertise, and I'm writing to let you know that we would like to send your submission out for external peer review.

IMPORTANT: Although you have submitted your paper as a full Research Article, we think that it would be better considered as a Short Report. In order to do this, you will need to reduce the number of main Figures to 4; please can you do this by either combining them or by moving some of them to the Supplement. I note that some of your Figures are very large and detailed, so if you're worried about this resulting in a loss of legibility, you could provide higher resolution versions of the main Figs in the Supplement. Please could you also select "Short Report" from the choice of article type? There is no need for any other formatting changes.

However, before we can send your manuscript to reviewers, we need you to complete your submission by providing the metadata that is required for full assessment. To this end, please login to Editorial Manager where you will find the paper in the 'Submissions Needing Revisions' folder on your homepage. Please click 'Revise Submission' from the Action Links and complete all additional questions in the submission questionnaire.

Please re-submit your manuscript within two working days, i.e. by Sep 11 2019 11:59PM.

During resubmission, you will be invited to opt-in to posting your pre-review manuscript as a bioRxiv preprint. Visit http://journals.plos.org/plosbiology/s/preprints for full details. If you consent to posting your current manuscript as a preprint, please upload a single Preprint PDF when you re-submit.

Once your full submission is complete, your paper will undergo a series of checks in preparation for peer review. Once your manuscript has passed all checks it will be sent out for review.

Feel free to email us at plosbiology@plos.org if you have any queries relating to your submission.

Kind regards,

Roli Roberts

Roland G Roberts, PhD,

Senior Editor

PLOS Biology

PLoS Biol. doi: 10.1371/journal.pbio.3000506.r002

Decision Letter 1

Roland G Roberts

21 Oct 2019

Dear David,

Thank you very much for submitting your manuscript "Patterns of smallpox mortality in London, England, over three centuries" for consideration as a Short Report at PLOS Biology. Your manuscript has been evaluated by the PLOS Biology editors, an Academic Editor with relevant expertise, and by four independent reviewers.

You'll see that all four reviewers are broadly positive about the study. However, reviewer #2 (a historical demographer) raises some substantial concerns about the historical aspects, including record-keeping practices over the years; please note that her main review is in the Word attachment. In addition, reviewers #3 and #4 ask for you to expand further on your analyses. Please can you attend to all the concerns raised.

In addition, I think I might've been a bit hasty in asking you to compress the Figures to fit our "Short Report" format. Given the overall enthusiasm expressed by reviewers #1, #3 and #4, the Academic Editor and I would be happy for you to re-expand the Figures and text (as needed) and change back to a full Research Article, should you wish.

In light of the reviews (below), we will not be able to accept the current version of the manuscript, but we would welcome resubmission of a much-revised version that takes into account the reviewers' comments. We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent for further evaluation by the reviewers.

Your revisions should address the specific points made by each reviewer. Please submit a file detailing your responses to the editorial requests and a point-by-point response to all of the reviewers' comments that indicates the changes you have made to the manuscript. In addition to a clean copy of the manuscript, please upload a 'track-changes' version of your manuscript that specifies the edits made. This should be uploaded as a "Related" file type. You should also cite any additional relevant literature that has been published since the original submission and mention any additional citations in your response.

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Upon resubmission, the editors will assess your revision and if the editors and Academic Editor feel that the revised manuscript remains appropriate for the journal, we will send the manuscript for re-review. We aim to consult the same Academic Editor and reviewers for revised manuscripts but may consult others if needed.

We expect to receive your revised manuscript within two months. Please email us (plosbiology@plos.org) to discuss this if you have any questions or concerns, or would like to request an extension. At this stage, your manuscript remains formally under active consideration at our journal; please notify us by email if you do not wish to submit a revision and instead wish to pursue publication elsewhere, so that we may end consideration of the manuscript at PLOS Biology.

When you are ready to submit a revised version of your manuscript, please go to https://www.editorialmanager.com/pbiology/ and log in as an Author. Click the link labelled 'Submissions Needing Revision' where you will find your submission record.

Thank you again for your submission to our journal. We hope that our editorial process has been constructive thus far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Roli

Roland G Roberts, PhD,

Senior Editor

PLOS Biology

*****************************************************

REVIEWERS' COMMENTS:

Reviewer #1:

[identifies himself as David N. Fisman]

This is a magnificent paper, and highly informative. It is mathematically sophisticated but clearly written and easily understood by non-mathematicians.

I have 2 minor comments:

1. Unless I'm mistaken, "prodrom" is not a variant spelling of "prodrome". At any rate, prodrome (with e) is the more familiar term.

2. Eczema vaccinatum isn't "severe eczema". It represents extensive cutaneous infection in individuals with pre-existing eczema or atopic dermatitis. This can happen with other viruses too (c.f., eczema herpeticum). Would revise terminology.

Reviewer #2:

[identifies herself as Romola Davenport]

IMPORTANT: More detailed comments from this reviewer are available in the attached, downloadable Word document.

This paper reports for the first time an analysis of high frequency counts of smallpox burials and deaths in London over almost 300 years. The authors juxtapose their analyses with historical factors, especially relating to the smallpox control measures, that they claim account for the major changes they identify in smallpox mortality matterns in London. The patterns presented are very interesting however the paper's conclusions are not justified by the method used. The method adopted relies on visual comparison of smallpox patterns with an historical timeline. This is unsatisfactory, but would suffice for an exploratory paper that was designed to point the way to further research. However at present the method is used with insufficient rigour with respect to data quality and historical accuracy.

I recommend that the authors make further adjustments to the smallpox burial data to correct for known shortcomings, and rewrite sections of the paper to enhance clarity and to acknowledge more fully the tenuous nature of some of the claims regarding the effects of smallpox control measures. These recommendations are set out more fully in an attached document.

Reviewer #3:

This article reports the first analyses of a deeply fascinating dataset: the records of smallpox mortality in London from 1664-1930. Digitizing and making publicly available this dataset is a tremendous advance in and of itself, as there are a large number of follow-up studies that will be able to explore different features of this dataset and use it to uncover the influences of demographic, social, and public health change on the dynamics of infectious disease. It is therefore an important contribution, worth publication in a journal with the exposure of PLoS Biology.

As a Short Report, I realize that the analyses do not necessarily need to be complete. And yet, I was left wanting more from even these preliminary analyses. In particular, the article goes into extensive detail about the history of smallpox in London, but the connection between the statistical analyses and this story is only explored in a very limited fashion. In particular, while Fig. 2 and Fig. 4 both annotate the data with major historical events that might be relevant to smallpox transmission and mortality, the discussion of the connection between any patterns observed in the data and these events in the Results or Discussion is very limited. For example, on lines 454-462, the authors note several timepoints where seasonality shifts, but those timepoints are not explicitly related back to any of the key events in the history of smallpox. Or, for another example, on lines 422-428, there is more connection between the regularity of epidemics and the history of variolation and vaccination, but there is no discussion of whether the patterns observed in the data (e.g. the shift to very regular epidemics with the introduction of variolation) make sense given the likely effects of control measures on transmission. This carries over into the Discussion as well, which was too brief given all of the potential for a very interesting discussion of a very interesting dataset.

I do think there is plenty of space available to expound on the connection between the statistical analyses and the historical transitions in both London's demography and the control of smallpox, as the historical sections can probably be shortened or eliminated without much loss. In particular, the entire section on "Types of Smallpox" (including Fig. 1) could be removed without loss of content, as none of the information in that section has any bearing on the analysis presented in the paper. Much of that information (e.g., on incubation periods and infectiousness) would be relevant to an paper attempting to fit an epidemiological model to the data, which I assume will happen in a follow-up paper. Similarly, the section, "Smallpox history" could also be drastically shortened: it is included only "to provide context" (line 27), but it is unclear to me how that context is actually helpful, given the detailed discussion of smallpox history in London that follows, especially in the "Annotation of data with historical events" section.

In sum, I think this is a very interesting dataset and analysis, and that some effort to tighten the connection between that analysis and the historical events discussed in the paper would make it a very valuable contribution.

Reviewer #4:

This is a unique and fascinating study on the long-term population dynamics of smallpox. The assembling and curating of such a long record with concurrent relevant events on the history of control is of major value to the field of population dynamics of infectious diseases in general.

I have however a number of comments intended to clarify the analyses and to strengthen the conclusions. I believe the authors should be able to address these, and to go further in the interpretation of the results and the kinds of questions this data set, unique in its length, will allow them or others to address in the future, given the results here and what is already known about seasonal SIR dynamics. On this last aspect, I have found the paper a bit thin.

1) The changes in seasonality are an important result. A main conclusion is a shift from summer to winter (line 490 Discussion). The analysis presented in Fig 4b is difficult to ‘see’. That is, one can read the caption and text but it is difficult to actually see the described patterns in the figure itself. This is because with so many years compressed in the x axis, one cannot easily follow where the main season is for a given year and how the trends go. I would recommend additional plots to make this sufficiently clear. For example, boxplots representative of the seasonal patterns in selected windows of time would help despite the non-stationarity of the ‘average’ seasonal cycle. (A smaller comment: the sentence on the zeros not being represented in the caption was confusing. The effect of the detrending needs to be clarified). Another important conclusion on the seasonality is in Line 471, where the authors write about changes in the strength of the annual power. I could not see where this comes from. The Fourier power spectrum averages over time, and as far as I could tell, the wavelet spectrum, which doesn’t, was applied after filtering the annual variation, so one cannot see there the non-stationarity of the annual power.

2) Another major result concerns the changes over time of the interannual variability; that is, the changes in the dominant periods of multi-annual cycles. These changes are interpreted as the consequence of control rather than birth rates (and contrasted to the importance assigned to demography in studies of other seasonal infectious diseases). This is where I would have liked to see a clearer exposition of why demography is not an important driver of the changes. From previous influential work on measles and childhood infections (including contributions of one of the authors, David Earn), we know that birth rates, transmission rates, and vaccination coverage, can have equivalent/related effects on seasonal SIR dynamics. How do the patterns/trends here relate to that previous knowledge and how can one infer the importance or dominance of control over demography?

3) Are there ways to look at the changes in the intensity of the annual cycle in relation to the importance of other, longer, cycles? We know from earlier theory how the spectrum of seasonal SIR dynamics should change with demography and transmission intensity. Are there concurrent patterns in how the power is distributed over different periods that would relate to that theory and allow interpretation?

4) Similarly, a major contribution of this paper will be to make this remarkable data set available to the community. The analyses in the paper itself are largely descriptive of trends in the seasonal and interannual variability and in relation to the timing of control efforts. It would be valuable to go further and based on these patterns, provide some major directions for what these data will allow going forward, in particular from their analyses with process-based models and related hypothesis about smallpox and seasonal SIR dynamics in general.

Attachment

Submitted filename: krylova and earn.docx

Click here for additional data file.^{(17.1KB, docx)}

PLoS Biol. 2020 Dec 21;18(12):e3000506. doi: 10.1371/journal.pbio.3000506.r003

Author response to Decision Letter 1

6 Jul 2020

Attachment

Submitted filename: KrylovaEarn2020_ResponseToReviewers.pdf

Click here for additional data file.^{(106.9KB, pdf)}

PLoS Biol. doi: 10.1371/journal.pbio.3000506.r004

Decision Letter 2

Roland G Roberts

10 Aug 2020

Dear Dr Earn,

Thank you for submitting your revised Research Article entitled "Patterns of smallpox mortality in London, England, over three centuries" for publication in PLOS Biology. I have now obtained advice from three of the original reviewers and have discussed their comments with the Academic Editor.

Based on the reviews, we will probably accept this manuscript for publication, assuming that you will modify the manuscript to address the remaining points raised by the reviewers. IMPORTANT: The article type still seems to be "Short Report"; please change it to "Research Article" when re-submitting. Please also make sure to address the Data Policy-related requests noted at the end of this email.

We expect to receive your revised manuscript within two weeks. Your revisions should address the specific points made by each reviewer. In addition to the remaining revisions and before we will be able to formally accept your manuscript and consider it "in press", we also need to ensure that your article conforms to our guidelines. A member of our team will be in touch shortly with a set of requests. As we can't proceed until these requirements are met, your swift response will help prevent delays to publication.

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REVIEWERS' COMMENTS:

Reviewer #2:

[identifies herself as Romola Davenport]

The authors have done a great job in revising the paper. It is much clearer and more tightly written, and presents a very impressive integration of historical and epidemiological literatures. I think it will make a great addition to current debates over the recent evolution of smallpox.

I have only minor comments that should be addressed before publication.

1. The authors are now perhaps too reticent in attributing causation, especially with respect to vaccination (page 14/33, lines 431-6). The decline in smallpox deaths with the introduction of vaccination in the early nineteenth century is very marked in both raw and normalised burials. This phenomenon was observed in other cities and states that adopted vaccination, and coincided with a marked decline in all-cause mortality (so the reduction in normalised smallpox burials is likely to underestimate the fall in smallpox mortality).

2. The term 'mortality' usually refers to mortality *rates*, that is, deaths per population at risk. The authors should distinguish clearly when they are talking about counts of deaths or normalised deaths, to avoid confusion. Figure 1 top panel should be labelled as smallpox deaths, not mortality, and the y-axis should read 'weekly smallpox deaths'. The y-axis of Figure 2 should also be labelled 'weekly all-cause deaths'.

3. A slightly larger comment: Why were normalised deaths used to study seasonal patterns? Seasonal patterns in raw deaths should be largely unaffected by longer-term changes in reporting units or under-registration (for the same reasons that normalised deaths are preferable for other purposes). The use of raw deaths to study seasonality would avoid the potential distortions caused by other seasonal patterns of mortality. For example, scarlet fever emerged as a major cause of death in London in the 1930s, with a marked autumnal pattern. This could have reduced the proportion of all deaths due to smallpox in the autumn, regardless of the underlying seasonal pattern of smallpox mortality in this period. Other important causes of death also showed seasonal patterns, and some of these changed over the period of the study (including measles). The authors should acknowledge this potential problem, if they prefer to use normalised burials and deaths.

4. Table 1 (appendix B): the labels for the third and fourth columns appear to be transposed.

5. page 3/33 line 51: another important element in the eradication of smallpox was the relatively low infectivity of smallpox.

6. page 3/33 line 60: insert 'and only for a few towns' between 'until later' and 'Bills of Mortality'.

7. page 4/33, line 81: perhaps replace 'exists' with 'survives' (to avoid the impression that patchy series necessarily imply gaps in the production of weekly bills as opposed to survival).

8. page10/33, line 256-7: perhaps add 'need for periodic revaccination' to the list of impediments to vaccine uptake. There was some resurgence of smallpox, and a rise in average age of victims, in the 1820s and 1830s that may have been associated with the waning of vaccine-derived immunity in birth cohorts in which vaccination was very common.

9. Typographical errors: abstract line 1, 'devastated' for 'devasted'; page 14/33, line 427: 'and' for 'an'; page 14/35, line 434: insert 'of' after 'introduction'.

Reviewer #3:

I appreciate the revisions that went into this manuscript, and I think it is very close to publication-ready at PLoS Biology. I remain convinced that the data, by itself, is incredibly valuable, and the extended analysis presented here makes this paper a more meaningful contribution as well. I have only a few comments that should be straightforward to address.

I feel that the importance (the "so what" question) of the analyses presented here needs to be better articulated in the Introduction and Discussion sections. Right now the value is implicit throughout the manuscript, and nowhere do the authors state clearly what they can learn from the statistical analysis of this data, and how will what they learn from these analyses be useful, both for understanding infectious diseases more generally and also for the next phase of work on smallpox specifically (e.g., building mechanistic models).

On the description of the handling of the heaped data, you might note that you considered other ways of handling the heaped data (e.g., the way it was handled in the first version of the manuscript) and that this did not have any effect on the conclusions drawn here.

The rationale for identifying the "Intervention uptake levels" in Fig. 1 is never made clear. Why, for example, does the assumed uptake level go from "very low" to "low" in 1728? Why does it go from "low" to "moderate" in 1740, if the first charitable variolation hospital didn't open until 1746? Etc. I realize that this doesn't impact the analyses presented here (because you are not seeking to draw any quantitative conclusions between the dynamics and the level of intervention uptake), but I still think it would be useful to provide some justification.

You do not justify the use of square-root transformation in the spectral analysis section. Also, in this section it would be useful to explain to a reader who has limited exposure to time series analysis what is gained by carrying out both the power spectrum analysis and the wavelet analysis.

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

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

The discussion of possible viral evolution (lines 551-559) could reference some of the theoretical work by Sylvain Gandon and Troy Day on how vaccination is expected to drive pathogen evolution (especially the reference on line 557-559 that suggests the potential for variolation to be "leaky"). E.g.,

Gandon, S., Mackinnon, M. J., Nee, S., & Read, A. F. (2001). Imperfect vaccines and the evolution of pathogen virulence. Nature, 414(6865), 751-756.

Gandon, S., & Day, T. (2007). The evolutionary epidemiology of vaccination. Journal of the Royal Society Interface, 4(16), 803-817.

To help foreshadow the future work you anticipate in response to these data and analyses, you might say a bit more about *how* the studies of measles and other childhood infections were able to explain dynamical transitions evident in the data (liens 583-588).

You are missing an "in" on line 610 between "patterns" and "infectious."

Reviewer #4:

The authors have done a great job at clarifying my questions and addressing my concerns in the revision. The revised presentation on the changes in seasonality and on the interannual variation is now very clear. I also appreciated the discussion on the directions these data and patterns open up for future research.

PLoS Biol. 2020 Dec 21;18(12):e3000506. doi: 10.1371/journal.pbio.3000506.r005

Author response to Decision Letter 2

13 Nov 2020

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PLoS Biol. doi: 10.1371/journal.pbio.3000506.r006

Decision Letter 3

Roland G Roberts

17 Nov 2020

Dear Dr Earn,

On behalf of my colleagues and the Academic Editor, Andy P. Dobson, I am pleased to inform you that we will be delighted to publish your Research Article in PLOS Biology.

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Data Availability Statement

All data are available at https://github.com/davidearn/London_smallpox and at the International Infectious Disease Data Archive at http://iidda.mcmaster.ca.

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PERMALINK

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

Olga Krylova

David J D Earn

Roles

Abstract

Introduction

Smallpox background

Data

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.

London Bills of Mortality

Fig 1. Example of one of the London Bills of Mortality.

Reporting of smallpox deaths

Transition to the Registrar General’s Weekly Returns

Heaping during the transition period

Missing weeks

Consistency checks

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.

London’s population

Table 1. Population of London, England (1550–1931).

Annotation of data with historical events

Control-free era

Early variolation, 1721 to 1740

Increasingly common variolation, 1740 to 1808

Industrial revolution

Vaccination

Better access and increasingly strong legislation concerning vaccination

Eradication in the 20th century

Methods

Normalization

Spectral analysis

Classical power spectrum

Wavelet spectrum

Seasonality

Results

Patterns in the raw time series

Normalization

Fig 4. Weekly all-cause deaths in London, England, 1661–1930.

Patterns in the normalized time series

Spectral analysis

Classical power spectrum

Fig 5. Classical Fourier power spectrum of the normalized weekly smallpox mortality time series for London, England, 1664–1930.

Wavelet spectrum

Fig 6. Spectral structure and seasonality of smallpox dynamics in London, England, 1664–1930.

Seasonality

Discussion

Previous work on smallpox dynamics in London

Fig 7. Periodicities in the time series of smallpox mortality in London, 1664–1930.

New data and descriptive statistics

Interpretations

Seasonality

Explaining transitions in smallpox dynamics

Conclusions

Acknowledgments

Abbreviations

Data Availability

Funding Statement

References

Decision Letter 0

Roland G Roberts

Roles

Decision Letter 1

Roland G Roberts

Roles

Author response to Decision Letter 1

Decision Letter 2

Roland G Roberts

Roles

Author response to Decision Letter 2

Decision Letter 3

Roland G Roberts

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

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