bioRxiv preprint doi: https://doi.org/10.1101/771220; this version posted September 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
Patterns of smallpox mortality in London, England, over three centuries
Olga Krylova1,2, David J.D. Earn1,3,*
1 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 2 Advanced Analytics, Canadian Institute for Health Information, Ottawa, Ontario, Canada K2A 4H6 3 M.G. DeGroote Institute for Infectious Disease Research, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Abstract
Smallpox is unique among infectious diseases in the degree to which it devasted 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 and the Registrar General’s Weekly Returns. We annotated the resulting time series with a sequence of historical events that appear to have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in smallpox dynamics changed over decades and centuries, and how these changes were related to control interventions and public health policy changes. We also examine how the seasonality of smallpox epidemics changed from the 17th to 20th centuries in London.
Keywords: smallpox; London Bills of Mortality; variolation; vaccination; power spectrum; wavelet transform; seasonality
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Introduction 1
Smallpox was declared eradicated 40 years ago [1], after unparalleled devastation of 2
human populations for many centuries [2,3]. Until the 19th century, smallpox is thought 3
to have accounted for more deaths than any other single infectious disease, even 4
bubonic plague and cholera [2–5]. In London, England, alone more than 320,000 people 5
are recorded to have died from smallpox since 1664. 6
Investigation of smallpox dynamics in the past is important not only for 7
understanding the epidemiology of a disease that has been exceptionally important in 8
human history, but also in the context of the potential for its use as a bioterrorist agent 9
in the future [6–10]. From the historical perspective, key issues include relationships 10
between patterns of smallpox outbreaks and demographic changes, uptake of 11
preventative measures, and interactions between epidemics and other historical events. 12
We examined 267 years of weekly smallpox mortality records from the city of 13
London, England, beginning in 1664. The data span an early era before any public 14
health practices were in place, the introduction of variolation and then vaccination, and 15
then the decline of smallpox mortality until it became an extremely unusual cause of 16
death. In addition to a statistical description of the temporal patterns in the data, we 17
present a timeline of major historical events that occurred during the epoch we studied. 18
Overlaying the historical timeline with smallpox mortality and prevention patterns 19
provides an illuminating view of three centuries of smallpox history. 20
Some previous work on smallpox dynamics in London has been based on annual 21
records [11,12], which lack the temporal resolution of the data we study, and 22
consequently smoothed out seasonal patterns that we identify. More recent work has 23
examined individual death records in a single London parish over a period of several 24
decades (1752–1805) and identified a decline in adult smallpox mortality risk after 25
1770 [13]. 26
To provide context, we briefly review the known history of smallpox, and describe its 27
natural history, before presenting and analyzing the data on which we focus. 28
Smallpox history 29
The origin of smallpox is not known. It appears to have coexisted with humans for 30
thousands of years, and is thought to have first appeared in Asia or Africa sometime 31
after 10,000 BC before spreading to India and China [2]. The earliest credible evidence 32
of smallpox existence in the ancient world comes from the Egyptian mummies of the 33
Eighteenth and Twentieth Dynasties (1570 to 1085 BC) [1, 2]. 34
After having established in Egypt, India and China, smallpox spread to Athens and 35
Persia. By the eighth century AD the virus had reached Japan in the East and Europe 36
in the West [2]. In the fifteenth century smallpox was widespread throughout 37
Europe [1]. The Spanish invasion of Mexico in the sixteenth century brought smallpox 38
to previously unexposed populations of the Aztec and Inca civilizations. Devastating 39
epidemics killed nearly half of the native population of Mexico in less than six months 40
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after its first appearance in April of 1520 [2]. Two centuries later, smallpox had become 41
a major endemic disease everywhere in the world. 42
Smallpox was directly responsible for the death of hundreds of thousands of people 43
each year during the Early Modern period (1500-1800) in Europe [3]. In many cases 44
surviving victims were left blinded or disfigured for life [14]. Smallpox also could have 45
been a major cause of infertility in male survivors [2,3]. The only defence against this 46
“speckled monster” was a procedure initially called inoculation, and now known by the 47
more specialized term variolation. It was introduced in Europe only in 1721 despite 48
being successfully used in China and India for centuries before. It can be described as 49
an injection of the smallpox virus taken from a pustule or dried scabs of a person 50
suffering from smallpox into a healthy individual [3]. The discovery of vaccination by 51
Edward Jenner in 1796 provided a safer and much cheaper alternative to variolation. 52
The original form of vaccination was an injection with cowpox virus, which also 53
provided immunity to smallpox. This discovery was a major milestone in modern 54
medicine as it laid the ground for all future vaccination strategies. Indeed, the word 55
“vaccine” takes its origin from the latin “vacca” meaning cow, and was first used by 56
Jenner to describe his new method of “vaccine inoculation” [15]. 57
The discovery of a vaccine was the key factor that made eradication of smallpox an 58
achievable goal. Other important factors were the absence of an animal reservoir, easy 59
recognition of the disease from its symptoms, and non-existence of asymptomatic 60
cases [16]. The World Health Organization launched its eradication campaign in 61
1967 [1,17]. Ten years later the world’s last endemic smallpox case was registered in 62
Somalia. In 1980, a Global Commission declared smallpox eradicated [18]. This was the 63
first disease to be eradicated entirely by human efforts. The only remaining viral 64
samples were stored in laboratories in Russia and the United States [9]. “The greatest 65
killer” [2] has never circulated since. 66
Unfortunately, the tragic events of September 11, 2001 and the anthrax scare of 2001 67
led to widespread concern about bioterrorism and, in particular, the use of smallpox as 68
a bioweapon. In fact, its high case fatality rate, person-to-person transmission, and 69
limited immunity in the population make smallpox even more dangerous than anthrax. 70
The US Centres for Disease Control and Prevention (CDC) classifies smallpox as a 71
Category A bioweapon agent [10,19]. 72
An increasing proportion of the world’s population lacks immunity to 73
smallpox [20,21]. As routine vaccination was stopped in the 1970s, most people born 74
since then are fully susceptible. In addition, the level of immunity in people vaccinated 75
before 1970 is unknown. Naturally acquired smallpox and variolation typically produce 76
life-long immunity. In contrast, the vaccinia virus, which is the basis of the modern 77
vaccine, provides complete immunity only for a short period of time, 3–5 years, after 78
which immunity wanes rapidly [1,22]. Long term vaccine-induced immunity is uncertain. 79
However, even after 20 years the case fatality rate in vaccinated persons is much smaller 80
than in the unvaccinated [1]. 81
The smallpox vaccine that was used until eradication is not considered safe, because 82
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of rare—but extremely dangerous—complications that include severe eczema, 83
postvaccinal encephalitis (inflammation of the brain), and significant risk of death. 84
During routine vaccination in the United States six to eight children died each year 85
because of various vaccine-induced complications [2, p. 294]. Moreover, smallpox 86
vaccination was not safe for people with weakened immune systems (e.g., pregnant 87
women, HIV-positive individuals and cancer patients). Consequently, mass vaccination 88
was ceased because the risks of complications were perceived to be much greater than 89
the risk of a bioterrorist attack. In recent years, new and safer vaccines have been 90
developed [23,24], which would likely be more pallatable to the population if mass 91
vaccination were reintroduced. 92
Until 2018, vaccination was the only available measure to protect against smallpox. 93
In July 2018, the U.S. Food and Drug Administration (FDA) approved a new antiviral 94
drug (tecovirimat) as the first drug intended to treat smallpox [25]. However, the 95
approval was based only on animal trials, as it was not feasible to conduct efficacy trials 96
in humans [10,26]. Therefore the actual efficacy of this drug in humans is unknown. 97
Types of smallpox 98
Smallpox is an acute, highly contagious and frequently fatal disease. The commonly 99
accepted term “small-pox” was first used in England at the end of the 15th century to 100
distinguish it from syphilis, which was known as “great-pox” [2, pp. 22–29]. 101
Smallpox is characterized by high fever and a distinctive skin rash that often leaves 102
pock scars after scabs fall off [14]. Infection usually occurs via the respiratory tract 103
through air droplets if exposure occurs from face-to-face contact with an infectious 104
person. Direct contact with virulent rash, bodily fluids, or bedding, blankets, or 105
clothing used by an infectious individual can also, in rare cases, result in smallpox 106
infection [2, p. 3] [1, pp. 121–168]. 107
Smallpox is caused by the Variola virus, which takes its name from the latin word 108
varius meaning spotted or varus meaning pimple. Variola is a member of the genus of 109
orthopoxviruses, which also includes cowpox, monkeypox, buffalopox, vaccinia and 110
many other members [2, p.6]˙ [1, pp. 69-120]. There are two distinct variants of Variola 111
that can cause smallpox: Variola major and Variola minor 112
[1, pp. 1–68] [2, pp. 3–9] [22, pp. 525–527]. These two smallpox variants differ 113
substantially in severity of symptoms and case fatality proportion. 114
Variola major, which had a case fatality of 5–25% and occasionally higher [1, p. 4], 115
was the only known smallpox type until the beginning of the 20th century. Based on 116
strain virulence and host response, a number of clinical types of V. major were 117
defined [1, pp. 1–121]: 118
• ordinary-type was the most common (about 80% of cases), with case fatality 119
20%; 120
• modified-type was milder, had an accelerated course of infection, and occurred 121
mostly in previously vaccinated persons; 122
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• variola sine eruption was rare, occurred in vaccinated persons through contact 123
with smallpox patients, and was characterized by a high fever without rash 124
eruption; 125
• flat-type was characterized by lesions that remained flat. It was rare and usually 126
fatal; 127
• haemorrhagic-type is distinguished from other types by especially severe 128
symptoms, a short incubation period, and high case fatality ∼ 96%. It was rare, 129
occurred mostly in adults, and at the early stage of infection was hard to 130
distinguish from ordinary-type or modified-type. 131
Variola minor, first recognized in 1904 [2], caused a milder, less virulent form of 132
smallpox and had a mortality rate of about 1% or less. Variola minor was the only 133
endemic type of smallpox present in England after 1920 [2, pp. 8, 97]; [1, pp. 243]. In 134
1935, England became smallpox-free for the first time in history, and further cases of 135
naturally acquired smallpox arose only from importation [2]. 136
Natural history of smallpox infection 137
The course of a single smallpox infection (its natural history) depends on the variant of 138
the virus, the clinical type, and the vaccination status of the host individual. Since the 139
ordinary-type of Variola major was the most common type of smallpox, we describe its 140
natural history here (Fig 1). 141
NO SYMPTOMS SYMPTOMS
Stage Incubation Period Prodrom Early Rash Pustular Rash Pustules & Scabs Resolving Scabs
Infectiousness None Rare Extreme Moderate Low
0 12 15 1922 24 28 35
Time, days
Point of Death Recovered Infection
Fig 1. The natural history of smallpox infection. The prodrom stage begins with fever but the patient is very rarely contagious. Early rash is the most contagious stage, when the rash develops and transforms into bumps. During the pustular rash stage bumps become pustules, then turn into scabs during the pustules and scabs stage, and finally fall off during the resolving scabs stage. The infected person is contagious until the last scab falls off.
There is an incubation period during which the infected person has no symptoms 142
and is not contagious. The duration of this stage can vary from 7 to 19 days, but in 143
most cases is about 12 days. The prodrom stage begins with the onset of fever, and 144
sometimes includes vomiting and diarrhea. The host is rarely contagious at this stage. 145
The rash appears 2–4 days after the onset of fever. It starts as small red spots on the 146
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tongue and in the mouth that grow into sores that break open within 24 hours of their 147
appearance. At this point, a large amount of virus is contained in the mouth and the 148
throat of the infected host, making them extremely contagious. Then the rash spreads 149
rapidly all over the body, and in a few days transforms into bumps filled with thick fluid. 150
This early rash stage continues for about 4 days. It is followed by a pustular rash stage 151
(average duration 5 days) during which the bumps become pustules. Over the next 5 152
days (pustules and scabs stage), pustules turn into scabs. The scabs fall off during the 153
resolving scabs stage (average duration 6 days), often leaving pock marks on the skin. 154
The overall duration of the illness is about 23 days [27]. In fatal cases, the majority of 155
deaths occur on the 10th–16th day from the beginning of symptoms [1, p. 22]. The usual 156
cause of death is severe toxemia, the release of toxins in the blood [1, p. 130] [28, p. 345]. 157
Data 158
We accessed original documents in London, England, in the Guildhall Library, the 159
British Library, the Wellcome Library, and the London Metropolitan Archive. We 160
digitized birth, death and population records for London throughout the period over 161
which smallpox was listed as a cause of death (1661–1934). The last smallpox death 162
reported in London was in the week of 24 February 1934. 163
All data analyzed in this paper are shown in Fig 2, and are available both in 164
supplementary material and at the International Infectious Disease Data Archive 165 1 (IIDDA, http://iidda.mcmaster.ca ). 166
London Bills of Mortality 167
Registration of deaths in England began in 1538 [29, p. 54], but systematic summaries of 168
deaths categorized by cause were not published until later, in the Bills of Mortality. 169
The Bills of Mortality included information about baptisms and church burials, 170
categorized by cause of death. The Company of Parish Clerks, who published the bills, 171
collected counts from the individual Anglican parish registers [30,31]. Weekly bills 172
began to be published frequently in 1604 [32], but not without large gaps until 1661. A 173 2 nearly continuous weekly sequence of bills exists starting 18 October 1664. 174
Reporting of smallpox deaths 175
Before 1701, smallpox was listed in the Bills of Mortality under the heading “flox and 176
smallpox”. “Flox” is an old term for the haemorrhagic type of smallpox [32, 33, p. 436]. 177
After 1701, “smallpox” was used consistently. Other disease names that occur in the 178
bills and are considered by some to be associated with smallpox are “flux” and “bloody 179
flux”. Razzell [3] suggested that bloody flux was a name used for haemorrhagic 180
1Please note that at the time of submission of this paper, the IIDDA web site is down while major restructuring is taking place. We hope this will be completed before the paper is published. 2Until 1752, New Years Day was 25 March in England. However, we always indicate years following the modern practice of defining New Years Day to be 1 January.
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smallpox, and that it was considered a distinct disease [3, p. 104]. However, 181
Creighton [32] described bloody flux as an old name for dysentery and not as something 182
related to smallpox [32, p. 774]. A Glossary of Archaic Medical Terms [33] also defines 183
“bloody flux” as dysentery and “flux” as diarrhea. In any case, mortality from “bloody 184
flux” and “flux” was negligible compared to smallpox (4,679 deaths in total from 185
“bloody flux” and “flux” compared to 322,219 total smallpox deaths). Consequently, 186
even if they were related to smallpox deaths, they would not significantly influence our 187
findings. We therefore used the sum of “flox and smallpox” and “smallpox” records and 188
did not include “bloody flux” and “flux” in our data. 189
Transition to the Registrar General’s Weekly Returns 190
The Bills of Mortality were the only official registration system used in England until 191
the introduction of national records, the Registrar General’s Weekly Returns, in 1837. 192
The necessity for improvement of the methods of data collection became evident at the 193
end of the 18th century. The accuracy of the old system of parish records had been 194
compromised by the rapid growth of London’s population from the beginning of the 195
industrial revolution. Parish clerks simply could not keep up with the increasing flow of 196
information. As a result, the Registrar General’s Office was created with the main 197
purpose of keeping birth and mortality records more complete, and covering all sectors 198
of the population [31]. 199
We used the Registrar General’s Weekly Returns from 1842 onwards. 200
Adjustments during the transition period 201
Throughout the period 1796–1842, the last week of the reported year, which was the 202
first week of December, had an unusually high number of reported deaths. The reason 203
for this appears to be backlog, i.e., that deaths that had occurred previously (but were 204
not counted at the time) were all reported in the first week of December. To address 205
this inaccuracy, we replaced the records showing strikingly high numbers of deaths with 206
the average of the previous and following weeks. Then the difference between the 207
original and the replaced values was uniformly distributed throughout the year to keep 208
the annual number of deaths consistent with the original data. 209
Missing weeks 210
The mortality bills for some weeks have been lost. Fortunately, all gaps are small 211
(typically 1–5 weeks) with the largest gap being 9 weeks. These gaps were replaced with 212
linearly interpolated values to obtain a time series without missing values. 213
Consistency checks 214
Annual summaries of mortality in London were published from 1629 onwards. Initially, 215
these were annual bills of mortality and later they were annual summaries of the 216
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Registrar General’s returns. Creighton [32] tabulated annual all-cause mortality 217
(1629–1837) and smallpox mortality (1629–1893). In Fig S2, we compare these annual 218
counts with annual aggregations of our weekly data. The data from the two sources 219
align well for most years. There are significant differences only during 1837–1841, which 220
was the period of transition of control of mortality summaries from the Company of 221
Parish Clerks to the Registrar General for England and Wales. 222
London’s population 223
Decennial censuses of London began in 1801 [34]. We estimated London’s population at 224
earlier times based on Finlay and Shearer [35] for the period before 1700 and 225
Landers [36] for 1700–1800. See Appendix. 226
Annotation of data with historical events 227
Over the 267 years that we study here, London underwent major demographic and 228
social changes, and there were a variety of historical events that may have had 229
substantial impacts on smallpox dynamics. The changes that were most obviously 230
relevant to smallpox dynamics were the introduction of smallpox control measures 231
(variolation and vaccination). Other potentially relevant events include wars and the 232
industrial revolution. We annotate the smallpox time series in Fig 2 with the major 233
events and developments that we described below. 234
Control-free era. The first recorded outbreak of smallpox in England is dated to 12 235
August 1610 [32, p. 435]. Smallpox became one of the major causes of death in England 236
in the 17th century, exceeding plague, leprosy and syphilis [2,31,36]. The impact of 237
smallpox did not change until preventative measures were introduced at the beginning 238
of the 18th century. 239
Early variolation, 1721–1740. Lady Mary Wortley Montagu (an influential writer 240
and poet [37]) is credited with introducing variolation to Great Britain [1–3, 17, 38]. She 241
had her daughter professionally variolated in London in April 1721. For the next two 242
decades, variolation occurred but was not popular. Only 857 people were variolated in 243
the whole of Great Britain from 1721 to 1727, and only 37 in 1728 [32]. After 1728, 244
precise numbers are unknown but assumed to be low. English medical practitioners 245
implemented variolation very crudely with deep incisions that caused severe symptoms, 246
morbidity, and high mortality of up to 2%. 247
Increasingly common variolation, 1740–1808. At the beginning of the 1740s, 248
only the rich could afford variolation. Charitable variolation began with the 249
establishment of the London Smallpox and Inoculation Hospital in 1746. 250
Until 1762, variolation was usually preceded by four to six weeks of preparation, 251
which included purging, bleeding, and a restricted diet with limited amount of food. 252
September 11, 2019 8/27 Septem England. in smallpox of history Fig Intervention bioRxiv preprint uptake 2. not certifiedbypeerreview)istheauthor/funder,whohasgrantedbioRxivalicensetodisplaypreprintinperpetuity.Itmadeavailable level Data London population Normalized smallpox mortality Timeline Weekly smallpox mortality e 1 2019 11, ber 100 250 290
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1780 1780 discovery Vaccine
1790 1790 1,080,000 High
1796 1796 1800 Low ● founded Establishment Vaccine National
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1914 War I World 1914 1918 1918 4,400,000 8,110,000 1924 19248,110,000 minor Variola 1931 ● ● 1931 1931● 10 10 10
1 2 3 Trend of weekly births weekly of Trend 9/27 bioRxiv preprint doi: https://doi.org/10.1101/771220; this version posted September 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
Fig 2. The top of the graph shows estimates of the London population for inner London (dashed black line) and all of London (solid black line). The top of the main panel (shaded) indicates the data sources. Smallpox mortality data were collected from two sources: i) London Bills of Mortality, where smallpox deaths were recorded from 1664 until 1701 under the name “flox and smallpox” (light blue background colour) and under the name “smallpox” (light yellow background colour) from 1701 until 1841; ii) Registrar General’s Weekly Returns (light grey background colour) used from 1842 until 1931. Intervention uptake levels are shown as coloured bars: yellow green-dark olive for variolation with yellow green indicating the lowest level and dark olive the highest; and yellow-red for vaccination with light yellow indicating the lowest level and red the highest level. Weekly smallpox mortality is presented in dark blue. The trend of weekly births are plotted in dark red. The transition from one registration system to another during 1796–1842 resulted in reduced accuracy. A dashed dark red line shows a fitted birth trend during this period. Below the main panel, we annotate the timeline of historical events related to smallpox history in England: black text indicates events that influenced uptake of control measures; brown text shows events that influenced human behaviour; dark green shows the period when data accuracy was reduced. The bottom panel shows a time plot of weekly smallpox mortality normalized by the trend of weekly all-cause mortality (see Fig S1). The trend of normalized smallpox mortality (solid black curve) was estimated by Empirical Mode Decomposition. Red dots denote the peaks of the epidemics of 1838 and 1871–1872, the most significant smallpox epidemics of the 19th century.
Variolation was followed by an isolation period of two or more weeks. Isolated 253
individuals were placed in purpose-built inoculation houses [1, 3, p. 255]. The 254
preparation period was shortened after Robert Sutton’s improvement of variolation 255
using light incisions in 1762. Sutton’s new method dramatically decreased the severity 256
of symptoms and death, and reduced the cost. Consequently, it became more common 257
to offer variolation to the poor population free of charge. 258
Sutton’s variolation technique spread quickly around England and became very 259
popular in rural areas. When a new epidemic appeared to be highly probable, “general 260
variolation” of entire villages and communities was performed. In large towns and cities 261
the situation was quite different [39]. In London, the use of variolation was irregular 262
and attempts to perform “general variolation” were sporadic and rare. 263
Poor Londoners were variolated only through Smallpox Charities. They performed 264
public variolation in batches, separately for males and females, 8–12 times a 265
year [32, p. 506]. The charities did not admit children under 7 years of age despite the 266
fact that the vast majority of smallpox cases at that time were in children under 3 years 267
of age. 268
The full extent of variolation in London after the Suttonian innovation is unclear. 269
The figures from London Hospital show that the number of variolated individuals 270
increased dramatically from 29 in 1750 to 653 in 1767 and 1084 in 1768 [32, p. 506]. 271
Based on a variety of historical reports, Razzel concluded that variolation gained 272
considerable popularity in London at the turn of the 19th century [3, p. 72]. We 273
consider uptake of variolation to have been moderate during 1740–1768, after which 274
update increased and reached a maximum during 1790–1808 [3,40]. 275
Industrial revolution. Beginning in the 1780s, the Industrial Revolution brought 276
thousands of immigrants to London and led to an increase in population density [41–43]. 277
Smallpox was probably always present in London, unlike rural settings, which were 278
relatively smallpox free between epidemics [1, 44]. Consequently, whereas most adults in 279
London would have acquired smallpox when young, immigrants from rural areas were 280
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more likely to have escaped infection, and therefore contributed continously to the flow 281
of susceptibles into London. The larger susceptible pool might explain the increasingly 282
severe smallpox outbreaks at the end of the 18th century, despite the growing 283
popularity of variolation (Fig 2). 284
Vaccination. The discovery of a vaccine by Edward Jenner in 1796 was the most 285
important event in the history of smallpox and was directly responsible for the eventual 286
eradication of the pathogen. At first, however, the idea of vaccination was met with 287
skepticism by the scientific and medical community [1,2]. Indeed, Jenner “was advised 288
not to send a record of his observations to the Royal Society, which was prepared to 289
refuse it, but to publish it as a pamphlet; and as a pamphlet it appeared in 290
1798” [45, p. 62]. 291
Unlike variolation, vaccination came with relatively little risk to the vaccinee, no 292
preparatory period, and much lower cost. Consequently, vaccination was adopted by the 293
public more quickly and widely than variolation ever was [1]. Nevertheless, there were 294
initially many challenges to overcome associated with ineffective vaccine distribution 295
and storage, shortage of cowpox virus, inadequate vaccine efficacy, and religious and 296
philosophical objections. Despite these difficulties, vaccine uptake rose and led to a 297
dramatic decline in smallpox mortality by the end of the 19th century (Fig 2). 298
Unfortunately, quantitative reports on early smallpox vaccine uptake are sorely 299
lacking. Vaccinations were poorly recorded until the end of the 19th century. Available 300
data are incomplete, uncertain and inconsistent. For example, the figures from the 301
London Smallpox and Inoculation Hospital show the percentage of vaccinated patients 302
admitted to the hospital increasing steadily from 32% in 1825 to 73% in 1856 [46, p. 114], 303
whereas the Royal Commission on Vaccination found that only 25% of newborns were 304
vaccinated by 1820 and about 70% in some parishes by 1840 [31]. Mooney [47] states 305
that during 1854–1856 the percentage of vaccinated infants might have ranged from 28% 306
to 81% based on one source, but that another source indicates that infant vaccination 307
rates for London during the period 1845–1890 were much lower than the national 308
average and never increased above 500 per 1,000 live births (i.e., 50%). There appear to 309
be no surviving records concerning vaccinations of older age groups during this period; 310
however, it is hypothesized that many adults escaped vaccination [46]. In Fig 2, we 311
indicate the qualitative pattern of change in vaccine uptake. 312
Better access and increasingly strong legislation concerning vaccination. 313
State involvement in the control of smallpox in England began with the foundation of 314
the National Vaccine Establishment in 1808. It provided free vaccination at its London 315
stations and distributed vaccine to other parts of England [48]. Around this time, the 316
London Smallpox and Inoculation Hospital ceased variolation and began vaccination in 317
greater numbers. Smallpox outbreaks over the next decade were very mild, which was 318
believed to be due to the growing popularity of vaccination. 319
A strikingly large smallpox epidemic occurred in London in 1837–1838, and exploded 320
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into a European wide pandemic [2]. The authorities in England realized that some 321
radical measures had to be taken, which led to the first Vaccination Act of 1840, 322
providing vaccination free of charge and banning variolation. It was followed by the 323
Vaccination Act of 1853, which made vaccination of every child during the first four 324
months of life compulsory. The Vaccination Act of 1867 introduced penalties for not 325
complying with compulsory vaccination. 326
The Franco-Prussian war, which began in late July 1870, is believed to have initiated 327
the worst pandemic of smallpox in all of Europe in the 19th century. It resulted in at 328
least 500,000 deaths. England alone lost more than 40,000 people. Thanks to 329
compulsory vaccination, fatality rates in England were three times lower than in Prussia, 330
Austria and Belgium [2, pp. 87–91]. The immediate response of the English government 331
to this devastating pandemic was the Vaccination Act of 1871, which enforced very 332
strict control (through the courts) of the implementation of the previous Acts. 333
In the second half of the 19th century, many vaccine-related challenges were resolved. 334 3 Arm-to-arm vaccination was the main method of vaccine distribution in the beginning 335
of the century. It was dangerous because it could transmit other diseases such as 336
syphilis, and was consequently outlawed in 1898 [2]. It was replaced by the new 337
technique of passing cowpox from cow to cow. The new method of vaccine distribution 338
was first introduced in Naples, Italy in 1843 [49, 50]. However it arrived in England only 339
in 1881. Another important discovery was made in 1891 by Monckton Copeman [50], 340
who demonstrated that adding glycerine to smallpox vaccine reduces bacterial 341
contamination, making it more efficacious and reliable. 342
Eradication in the 20th century. The last large outbreak of Variola major 343
occurred in London in 1901–1902 (Fig 2) and was probably seeded from another 344
country [46]. After 1902, only very small outbreaks occurred with very low incidence 345
and very few deaths. 346
In 1967, the World Health Organization launched its global smallpox eradication 347
campaign, and by 1980, smallpox was certified as the first infectious disease to be 348
eradicated by human efforts [14]. 349
Methods 350
We used a variety of methods to elucidate the patterns in the London smallpox time 351
series. Spectral analyses and a visualization of seasonality allow us to reveal important 352
characteristics of the data that cannot be gleaned by inspection of the raw time plot 353
(Fig 2). 354
3Arm-to-arm vaccination was the method of vaccine distribution, which involved vaccine transfer from the infectious pustule of vaccinated individual to a non-vaccinated individual, and so on [1].
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Normalization 355
To control for changes in population size, city boundaries and data collection methods, 356
we normalized the smallpox data by the trend of the weekly all-cause mortality in 357
London. To calculate the trend, we used Empirical Mode Decomposition (EMD), 358
which is designed to identify trends in nonlinear and highly non-stationary time 359
series [51–53]. EMD was developed to overcome the drawbacks of moving averages, 360
other linear filters, or linear regression, which often perform poorly on non-stationary 361
data. EMD decomposes a signal into several components with a well defined 362
instantaneous frequency via “intrinsic mode functions” (IMF). IMFs are basically 363
zero-mean oscillation modes present in the data: the first IMF captures the high 364
frequency (shorter period) oscillations while all subsequent IMFs have lower average 365
frequency (longer period). Each IMF is extracted recursively starting from the original 366
time series until there are no more oscillations in the residue. The last residual 367
component of this process can be considered an estimate of the trend [52]. 368
Spectral analysis 369
We used spectral analyses to identify the strongest periodicities in the smallpox time 370
series. 371
Classical power spectrum 372
We computed the standard power spectral density [54–57] of the entire (normalized 373
and square root transformed) smallpox time series to obtain a global estimate of its 374
frequency content. We employed a standard modified Daniell smoother using the 375
spec.pgram function in R [58]. 376
Wavelet spectrum 377
Because infectious disease time series are typically highly non-stationary, wavelet 378
analysis has become increasingly popular in epidemiological research [59–64]. We 379
computed a wavelet transform [65, 66] of the (normalized and square root 380
transformed) smallpox time series in order to examine how smallpox periodicities 381
changed over the course of the three centuries. 382
A wavelet transform is computed with respect to a basic shape function, the 383
analyzing wavelet, which has a scale parameter that controls its width. Narrower (wider) 384
scales correspond to higher (lower) frequency modes in the time series. At any given 385
time and scale, a stronger correlation between the analyzing wavelet and the signal 386
yields a larger value of the wavelet transform. We obtain a complete (two-dimensional) 387
time-frequency representation of the data by convolving the analyzing wavelet—at each 388
scale—with the original time series. We used the Morlet wavelet [66] as the analyzing 389
wavelet to obtain the wavelet transform of the smallpox time series. 390
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The standard computation of the wavelet spectrum requires that the number of 391
points in the time series be a power of 2. Consequently, we pad the ends of the time 392
series with zeros to bring the number of time points in the data to the nearest power of 393
2. The resulting artificial discontinuity where the zero-padding begins reduces the 394
accuracy of the wavelet transform at the ends of the time series. Regions of lower 395
accuracy are identified by the “cone of influence”. Data outside this cone should be 396
interpreted with caution. 95% confidence regions are computed based on 1,000 Markov 397
bootstrapped time series [60,61]. 398
Seasonality 399
An indication of underlying seasonality in a time series is the occurrence of a spectral 400
peak at a period of one year. However, this crude measure suppresses the detailed 401
seasonal pattern and, in particular, does not reveal the times of year when peaks or 402
troughs occur. Following Tien et al [67], we visualized the evolving seasonal pattern of 403
smallpox dynamics with a heat map in the time-of-year vs. year plane. 404
Results 405
The time plot of the raw data (Fig 2) displays substantial changes in the structure, 406
amplitude, and frequency of smallpox epidemics over time. However, some of the 407
apparent changes are misleading because they do not account for population growth and 408
inconsistency of data sources. For example, the epidemic of 1871 appears to be the 409
largest, but it was not the largest relative to population size. In contrast, the epidemic 410
of 1838, which is frequently mentioned in the literature [2, 32], is not easily identifiable 411
in the raw data, likely because it occurred just at the time of transition between the 412
Bills of Mortality and the Registrar General’s Returns. 413
Normalization 414
Fig S1 shows the trend of weekly all-cause mortality in London (1661–1930) computed 415
with EMD. The bottom panel of Fig 2 shows the weekly London smallpox time series 416
normalized by the all-cause trend. 417
The normalized time series provides a more consistent and informative 418
representation of smallpox dynamics in London. For example, the epidemic of 1838 is 419
now easily identifiable, and the epidemic of 1871–1872 is much less extreme in 420
magnitude compared with other epidemics of the 19th century. 421
From the earliest times in the series, there were large, recurrent epidemics. More 422
common variolation after 1770 is correlated with stricter regularity of epidemics, while 423
the introduction of vaccination is associated with a dramatic reduction in the amplitude 424
of epidemics. During the period when variolation and vaccination were both in use 425
(1796–1840), the data appear to be noisier, and outbreaks occurred more frequently. 426
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After variolation was banned in 1840, inter-epidemic intervals increased and epidemic 427
peak heights declined, except for three large epidemics in 1871, 1876 and 1902. 428
The bottom panel of Fig 2 also shows the general trend of smallpox mortality over 429
the centuries (computed with EMD). This trend indicates that per capita smallpox 430
mortality increased steadily from 1664 until approximately 1770, after which there was a 431
gradual decline until its complete elimination. The begining of the decline is coincident 432
with the growing popularity of variolation. London’s population grew by an order of 433
magnitude over the subsequent years from 1796 when the vaccine was discovered until 434
1930; yet smallpox mortality in the city fell to negligible levels as vaccine uptake rose. 435
Spectral analysis 436
Classical power spectrum 437
Fig 3 shows the period periodogram (power spectrum as a function of period) for the 438
full smallpox time series. A strong peak at one year suggests underlying seasonality of 439
epidemics. Other peaks (near 2.2, 2.4, 3, 5.1 and 6 years) suggest more complex 440
dynamical patterns. 441
● 2.2 0.6 0.5 0.4
● 1 ● 3 ● 2.4 0.3 Spectral density Spectral 0.2 ● 5.1 ● 6 0.1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Period, years
Fig 3. Classical Fourier power spectrum of the normalized weekly smallpox mortality time series for London, England, 1664–1930. Before computing the power spectrum the time series was detrended and square root transformed [54]. The spectrum was smoothed using a modified Daniell window (weighted moving average) [54].
Wavelet spectrum 442
The bottom panel of Fig 4 shows the wavelet transform of the London smallpox time 443
series. Colours indicate strength of signal at given periods (blue meaning weak and red 444
meaning strong). The cone of influence and 95% confidence contours are shown in black. 445
The white curves in bottom panel of Fig 4 highlight the period with greatest power 446
at each timepoint. From 1664 until 1700 the dominant period was 3–4 years. Around 447
1705, it shifted to 2–3 years. After the introduction of variolation, wavelet power 448
weakens overall and the dominant period lengthens. From around 1740 to 1770, a 3-year 449
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mode dominates. Between 1770 and 1810, both one year and 2–3 year periods are 450
strong. After 1820, annual power is much less clear, and after 1840 the major period 451
smoothly drifted into a longer cycle of 3–4, and then 4–8 years. 452
Seasonality 453
The middle panel of Fig 4 shows the seasonal structure of smallpox mortality in 454
London. Until 1740, the maximum number of smallpox deaths occurred in the summer 455
or autumn. Then, until about 1770, outbreak peak times shifted to winter. After 1770, 456
the majority of deaths occurred in the autumn and winter. Epidemic patterns became 457
much less regular and less seasonal during the period 1808–1840. From the beginning of 458
the data set until 1840, smallpox mortality was lowest in the spring. After 1840, as 459
vaccination levels gradually increased, epidemics became strictly regular, with the 460
majority of deaths occurring in winter and spring. After the exceptionally large 461
epidemic of 1871, smallpox epidemics became extremely irregular and noisy. 462
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Fig 4. Spectral and seasonal structure of smallpox dynamics in London, England (1664–1930). Top panel: Weekly smallpox mortality normalized by the trend of all-cause mortality together with variolation and vaccination uptake levels, with red dots highlighting the major peaks in the time series (identified by visual inspection). Middle panel: Seasonality of smallpox epidemics. The normalized smallpox time series was detrended and square root-transformed before constructing the heat map. Dark red dots indicate the week of each year with the highest value of normalized smallpox mortality (as in the time series in the top panel). Zeros are not necessarily displayed with dark blue, because the detrending shifts the end of the time series up. Bottom panel: Wavelet transform of the normalized weekly smallpox mortality time series (square root-transformed and normalized to unit variance). The white curves show the local maxima of the wavelet power (squared modulus of wavelet coefficients [61, p. 291] at each time). The colours of the wavelet diagram vary from dark blue for low power to dark red for high power. The thin black line indicates the 95% confidence region, estimated from 1000 bootstrapped time series generated by the method of [61, pp. 292–293]. Below the “cone of influence” [61, 66], the calculation of wavelet power is less accurate because it includes edges of the time series that have been zero-padded to make the length of the series a power of 2. The wavelet spectrum was computed using MATLAB code kindly provided by Bernard Cazelles. As in Fig 2, the graph is annotated with the timeline of historical events related to smallpox history in England. September 11, 2019 17/27 bioRxiv preprint doi: https://doi.org/10.1101/771220; this version posted September 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
Discussion 463
We have digitized and analyzed what is, to our knowledge, the longest existing weekly 464
time series of infectious disease mortality. The timespan of the data, from 1664 to 1930, 465
covers an extraordinary period in London, England, during which smallpox changed 466
from a terrifying and unavoidable danger to an easily preventable infection. 467
Previous studies of smallpox dynamics in London were based on annual mortality 468
records [12,44,68], which preclude the detection of seasonal patterns. Our spectral 469
analysis revealed the presence of annual periodicity through the smallpox time series, 470
and changes in the strength of annual power are correlated with changes in control 471
practices. The previous work [12,44,68] attributed changes in inter-epidemic intervals to 472
changes in birth rates and nutrition; while these factors are likely to have influenced 473
smallpox dynamics in London, the correlations we have highlighted between the uptake 474
of preventative measures (and related legislation) and the observed changes in epidemic 475
patterns, strongly suggest that transitions in epidemic patterns were primarily driven by 476
control interventions. 477
Seasonal forcing of infectious disease transmission can stimulate persistence of 478
complex epidemic cycles [69] and chaos [70]. The mechanistic origin of seasonal forcing 479
may [71] or may not [72] be easy to determine. In the case of smallpox, previous 480
work [1,12,73] found that in temperate climates the majority of smallpox cases occurred 481
in the winter and spring, whereas in tropical climates the seasonality was less 482
pronounced. The general conclusion was that smallpox incidence always increases when 483
the weather is cool and dry; this belief influenced the planning of the eradication 484
campaign in India and seemed to help to improve its efficiency [1, pp. 179–181]. 485
Previous smallpox seasonality studies were mainly based on data from the 19th and the 486
20th centuries, when preventative measures were already common [1,73]. Our data set 487
is of a particular interest in this respect since it includes a period when only naturally 488
acquired smallpox immunity existed. Consequently, we were able to compare early and 489
later periods (which displayed a shift from summer to winter epidemics) and comment 490
on the impact that intensive preventive measures appeared to have on smallpox 491
seasonality (much greater regularity until smallpox deaths were mostly eliminated). 492
Better control is naturally expected to lead to less death. However, how 493
interventions influence the frequency structure and seasonality of epidemic time series 494
over decades and centuries is much more subtle [56, 74, 75]. While preliminary work has 495
been promising [76], careful estimation [77,78] and analysis [75,79] of patterns of 496
seasonal forcing will be required in order to use mechanistic models reliably to 497
explain [64] the observed transitions in smallpox transmission dynamics. 498
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Appendix: Population of London (1550–1931) 499
Finlay and Shearer [35] estimated the total population of London for every half century 500
from 1500 until 1700 based on information about the population north and south of the 501
river Thames, taking into account inaccuracies in data collection. Their book [35] also 502
contains data for other years, which was not included in their summary table. We 503
included those additional data in our study as well. Note that Finlay and Shearer 504
estimate for 1650 appears to be inaccurate due to an arithmetic error (it should be 505
≈400,000 instead of 375,000 according to their own figures). Population data for 506
1700–1800 were taken from Landers [36], who estimated the population for every decade 507
from 1730 until 1800. Census data, which is available for each decade since 1801, were 508
the source of remaining values [34]. The resulting data set of population estimates is 509
plotted in the top panel of Fig 2. 510
Year Total London Outer London Inner London Source 1550 120,000 120,000 [35] 1560 140,800 140,800 Estimated1 1580 180,400 180,400 Estimated1 1600 200,000 200,000 [35] 1620 297,000 297,000 Estimated1 1640 390,500 390,500 Estimated1 1650 391,450 391,450 Estimated1 1660 392,400 392,400 Estimated1 1680 468,600 468,600 Estimated1 1700 490,000 490,000 [35] 1735 660,000 660,000 [36] 1745 670,000 670,000 [36] 1750 675,000 675,000 [35] 1755 680,000 680,000 [36] 1765 730,000 730,000 [36] 1775 780,000 780,000 [36] 1785 859,234 826,502 [36] 1795 1,007,703 909,507 [36] 1801 1,096,784 959,310 137,474 [34] 1811 1,303,564 1,139,355 164,209 [34] 1821 1,573,210 1,379,543 193,667 [34] 1831 1,878,229 1,655,582 222,647 [34] 1841 2,207,653 1,949,277 258,376 [34] 1851 2,651,939 2,363,341 288,598 [34] 1861 3,188,485 2,808,494 379,991 [34] 1871 3,840,595 3,261,396 579,199 [34] 1881 4,713,441 3,830,297 883,144 [34] 1891 5,571,968 4,227,954 1,344,014 [34] 1901 6,506,889 4,536,267 1,970,622 [34] 1911 7,160,441 4,521,685 2,638,756 [34] 1921 7,386,755 4,484,523 2,902,232 [34] 1931 8,110,358 4,397,003 3,713,355 [34]
Table 1. Population of London, England (1550-1931).
1Estimated based on [35, Tables 2, 3] data.
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Acknowledgments 511
The data were photographed and/or entered primarily by Kelly Hancock, Claire Lees, 512
James McDonald, Laxmi Pandit, and David Richardson. Valerie Hart facilitated work 513
at the Guildhall Library in London. We were supported by the Natural Sciences and 514
Engineering Research Council of Canada (O.K. by an NSERC Postgraduate Scholarship 515
and D.E. by an NSERC Discovery grant). Early stages of this research were supported 516
by a J. S. McDonnell Foundation Research Award to D.E. 517
(https://www.jsmf.org/grants/d.php?id=2006014). We thank all members of the 518
Mathematical Biology Group at McMaster University for helpful comments and 519
discussions. 520
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SUPPLEMENTARY FIGURES
Normalization 703
London bills of mortality Registrar General's Weekly Returns 8000 4000 3000 2000 Weekly all cause mortalityWeekly 1000 0
1660 1680 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920
Years
Fig S1. Weekly all-cause mortality and its trend; London, England, 1661–1930. The trend was estimated by Empirical Mode Decomposition applied separately to the periods 1661–1842 and 1842–1930, which correspond to different data sources. The highest peak in all-cause mortality occurred during the Great Plague of London in 1665, which killed more than 8,000 people in the most severe week.
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Data consistency check 704
6000 Annual smallpox mortality: Annual Bills of Mortality, 1629−1893 (Creighton 1965) Annual sums of Weekly Bills of Mortality, 1664−1930 5000
4000
3000
Smallpox deaths Smallpox 2000
1000
0 1629 1634 1639 1644 1649 1654 1659 1664 1669 1674 1679 1684 1689 1694 1699 1704 1709 1714 1719 1724 1729 1734 1739 1744 1749 1754 1759 1764 1769 1774 1779
6000
5000
4000
3000
Smallpox deaths Smallpox 2000
1000
0 1780 1785 1790 1795 1800 1805 1810 1815 1820 1820 1830 1835 1840 1845 1850 1855 1860 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 1925 1930 Fig S2. Annual smallpox mortality data in London, England: 1629–1779 (top panel) and 1780–1930 (bottom panel). The data were gathered from two sources: the Annual Bills of Mortality tabulated by Creighton [32] and annual sums of our weekly counts from the weekly Bills of Mortality and the Registrar General’s Weekly Returns. Differences between the two data sets are indicated with white stacked bars if values in the Annual Bills are larger, and black stacked bars if corresponding annual sums from the weekly bills are larger. Note that no smallpox mortality data for the period 1637–1646 were available [32].
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