On 18 March,
the UK Government – led by the hapless and demonstrably increasingly incompetent
and out-of-his-depth prime
minister, Boris Johnson (along with its two technical advisors on the
Coronavirus threat, chief medical officer Chris Witty, an academic
epidemiologist at the London School of
Hygiene & Tropical Medicine, and chief scientific officer, Sir Patrick
Vallance, former president of research (
2012-17) at GlaxoSmithKline(GSK) , the multinational pharmaceutical giant, executed a very public policy U-turn, and decided to close all schools in England to virtually all pupils for an indefinite
period, starting tomorrow.
At a follow
on lunchtime press conference today, Sir Patrick unconvincingly attempted to
argue the basic facts on the ground had changed, so the policy changed. (www.theguardian.com/politics/live/2020/mar/19/uk-coronavirus-live-boris-johnson-london-lockdown-williamson-refuses-to-rule-out-government-putting-london-in-lockdown-by-weekend)
But had they?
An academic paper published 8 years ago (‘Effects of School Closure on Incidence of Pandemic Influenza in
Alberta, Canada,’ Annals of Internal Medicine, 7 February 2012; https://annals.org/aim/fullarticle/1033342/effects-school-closure-incidence-pandemic-influenza-alberta-canada) summarised the findings thus:
“The ending and restarting of school terms had a major
effect in attenuating the first wave and starting the second wave of pandemic
influenza cases. Mathematical models suggested that school closure reduced
transmission among school-age children by more than 50% and that this was a key
factor in interrupting transmission. The models also indicated that seasonal
changes in weather had a significant effect on the temporal pattern of the
epidemic.”
The authors concluded:
“Analysis of
data from unrestricted virologic testing during an influenza pandemic provides
compelling evidence that closing schools can have dramatic effects on
transmission of pandemic influenza. School closure seems to be an effective
strategy for slowing the spread of pandemic influenza in countries with social
contact networks similar to those in Canada.”
The paper - whose Primary Funding Sources were the Canadian
Institutes of Health Research, Natural Sciences and Engineering Research
Council of Canada, and Public Health Agency of Canada – which had six Canada–based
academic and medical professional authors, includes 51
footnote references, and is a highly reputable study
I wonder why the
UK Prime minister’s team seem no to be unaware of this study, or if they were,
why did they overlook its important conclusions?
Annex
Abstract
Background:
Control of
pandemic influenza by social-distancing measures, such as school closures, is a
controversial aspect of pandemic planning. However, investigations of the
extent to which these measures actually affect the progression of a pandemic
have been limited.
Objective:
To examine
correlations between the incidence of pandemic H1N1 (pH1N1) influenza in
Alberta, Canada, in 2009 and school closures or weather changes, and to
estimate the effects of school closures and weather changes on pH1N1
transmission.
Design:
Mathematical
transmission models were fit to data that compared the pattern of confirmed
pH1N1 cases with the school calendar and weather patterns.
Setting:
Alberta,
Canada, from 19 April 2009 to 2 January 2010.
Data Sources:
2009
virologic test results, 2006 census data, 2009 daily temperature and humidity
data, and 2009 school calendars.
Measurements:
Age-specific
daily counts of positive results for pH1N1 from the complete database of
35 510 specimens submitted to the Alberta Provincial Laboratory for Public
Health for virologic testing from 19 April 2009 to 2 January 2010.
Results:
Limitations:
Data probably
represent a small sample of all viral infections. The mathematical models make
simplifying assumptions in order to make simulations and analysis feasible.
Editors' Notes
Context
- Whether schools
should close during influenza epidemics is controversial. In 2009, testing
for influenza A(H1N1) was performed for many months in Alberta, Canada. A
mathematical model of H1N1 transmission was then constructed by using
those virologic data, as well as census data, climate records, and school
calendars.
Contribution
- School closure was
associated with reduced transmission among schoolchildren by more than
50%, attenuating the first wave of the H1N1 epidemic. The reopening of the
schools probably initiated the second H1N1 influenza wave. Seasonal
changes in weather also affected the epidemic pattern.
Caution
- Mathematical models
simplify reality.
Implication
- Closing schools may
slow the spread of influenza epidemics.
—The Editors
Social-distancing
measures feature prominently in analyses of pandemic preparedness and
management strategies 5, and school closure is one of the
most frequently considered measures 5. Influenza incidence and mortality
data do not typically show obvious effects of school closures, but several
studies 5,5,5 have used mathematical models to infer
that closing schools reduced transmission in various situations, including the
first phase of the 2009 influenza pandemic in Hong Kong 5. Here, we present the effects of
closing schools in Alberta, Canada, during the 2009 pandemic. The effects are
visually apparent in the data and confirmed by transmission modeling.
The 2009
pandemic emerged first in Mexico in April 2009 5. The subtype of the new virus
(A/H1N1) was the same as the 1918 pandemic strain, descendants of which have
circulated continuously since 1977 5. However, the new pandemic H1N1
(pH1N1) virus was sufficiently antigenically novel in humans that preexisting
immunity seemed to be weak or absent in most persons 5. The World Health Organization
declared the outbreak to be a pandemic on 11 June 2009 5. By the end of December 2009, more
than 12 000 deaths and more than 600 000 laboratory-confirmed cases
of pH1N1 had been reported worldwide 5,5. The World Health Organization declared
the pandemic to be over on 10 August 2010.
As the first
wave of the pandemic grew in intensity, many public health laboratories were
overwhelmed and implemented stringent eligibility restrictions for respiratory
virus testing 5. In Alberta, a large Canadian
province with a population of 3.7 million, no such restrictions were
implemented until the middle of the second wave of the pandemic. As a result,
from 20 April 2009 (when the first laboratory-confirmed pH1N1 sample was
collected) to 30 October 2009 (when restricted testing commenced 5), reported laboratory-confirmed
cases of pH1N1 in Alberta were not biased by sampling restrictions.
Population-level
analyses have indicated that pH1N1 has weak to moderate transmissibility 5,5,5,5,5, which makes it plausible that
social-distancing measures had a substantial effect on epidemic speed and
spread, as is suggested to have occurred during the 1918 influenza pandemic 5,5,5. In North America, the school year ended
in June 2009, during the first wave of the pandemic. We examine the incidence
pattern of pH1N1 in Alberta together with the pattern of classes ending for the
summer and investigate whether they are associated.
David J.D.
Earn, PhD; Daihai He, PhD; Mark B. Loeb, MD, MSc; Kevin Fonseca, PhD; Bonita E.
Lee, MD, MSc; Jonathan Dushoff, PhD
Author,
Article, and Disclosure Information
Acknowledgment: The authors thank Shamir Mukhi for his
contributions to the development of Data Integration for Alberta Laboratories
(DIAL); Jutta Preiksaitis and Marie Louie for their support of the DIAL
project; Rhonda Gordon for providing surveillance data; Marek Smieja, Joe Tien,
Ann Herring, and Raluca Eftimie for their comments; and Susan Marsh-Rollo for
her assistance with the acquisition of school schedules and weather data.
Grant
Support: By the
Canadian Institutes of Health Research, the Natural Sciences and Engineering
Research Council of Canada, and the Public Health Agency of Canada.
Potential
Conflicts of Interest: Disclosures can be viewed at www.acponline.org/authors/icmje/ConflictOfInterestForms.do?msNum=M11-1844.
Reproducible
Research Statement:Study protocol: Not available. Statistical code:
Available from Dr. He (e-mail, daihai@math.mcmaster.ca). Data set:
Available at the International Infectious Disease Data Archive (http://iidda.mcmaster.ca).
Requests for
Single Reprints: David J.D.
Earn, PhD, Department of Mathematics and Statistics, McMaster University, 1280
Main Street West, Hamilton, Ontario L8S 4K1, Canada; e-mail, earn@math.mcmaster.ca.
Current
Author Addresses: Drs. Earn and He: Department of Mathematics and
Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S
4K1, Canada.
Dr. Loeb:
McMaster University, MDCL 3200, 1200 Main Street West, Hamilton, Ontario L8N
3Z5, Canada.
Dr. Fonseca:
Department of Microbiology and Infectious Diseases, University of Calgary, 3330
Hospital Drive Northwest, Calgary, Alberta T2N 4N1, Canada.
Dr. Lee:
Edmonton Clinic Health Academy, 11405 87 Avenue, Room 3-593, Edmonton, Alberta
T6G 1C9, Canada.
Dr. Dushoff:
Department of Biology, McMaster University, 1280 Main Street West, Hamilton,
Ontario L8S 4K1, Canada.
Author
Contributions: Conception
and design: D.J.D. Earn, M.B. Loeb.
Analysis and
interpretation of the data: D.J.D. Earn, D. He, J. Dushoff.
Drafting of
the article: D.J.D. Earn, J. Dushoff.
Critical
revision of the article for important intellectual content: D.J.D. Earn, M.B.
Loeb, B.E. Lee, K. Fonseca, J. Dushoff.
Final
approval of the article: D.J.D. Earn, D. He, M.B. Loeb, B.E. Lee, K. Fonseca,
J. Dushoff.
Statistical
expertise: D. He, J. Dushoff.
Obtaining of
funding: D.J.D. Earn, M.B. Loeb.
Administrative,
technical, or logistic support: M.B. Loeb, K. Fonseca.
Collection
and assembly of data: K. Fonseca, B.E. Lee.
- From McMaster
University, Hamilton, Ontario; University of Calgary, Calgary, Alberta;
and Edmonton Clinic Health Academy, Edmonton, Alberta, Canada.
Methods
Surveillance Data
The Alberta
Provincial Laboratory for Public Health (ProvLab) tests for respiratory viruses
at the request of hospitals, community physicians, and a sentinel physician
network (The Alberta Recording and Research Network [TARRANT]) or in response
to respiratory outbreaks monitored by public health. During the 2009 influenza
pandemic, all samples submitted to regional laboratories for respiratory virus
testing were referred to ProvLab for comprehensive molecular testing for
influenza A; testing included an in-house validated reverse transcriptase
real-time polymerase chain reaction test for influenza A and B or the xTAG
Respiratory Virus Panel assay (Luminex Molecular Diagnostics, Toronto, Ontario,
Canada) 5. We obtained testing data by using
the Data Integration for Alberta Laboratories application 5, a Web-based, user-specific, secure
platform that has automatic data extraction and interpretation processes for
respiratory virus testing data at ProvLab (including testing results and
patient sex, age, and geographic information).
During the
pandemic, specimens were submitted to ProvLab from both community-based health
providers (including general practitioners, family physicians, and
pediatricians) and hospitals (emergency departments, hospital clinics, and
patient care units). Health facilities in the province instituted strict
infection-control practices at the beginning of the pandemic, which did not
change during its course. Until 30 October 2009, all specimens submitted to
ProvLab were tested. After 30 October 2009, respiratory virus testing was
restricted to patients awaiting hospital admission; hospitalized patients;
specimens from outbreak investigations, as requested by public health
officials; and specimens noted by the TARRANT surveillance program (<5% of
specimens).
Weather Data
We downloaded
daily average air and hourly air temperatures and dew points from Environment
Canada (www.weatheroffice.gc.ca/canada_e.html).
We used the hourly data to calculate hourly absolute humidity (Supplement) and averaged these values to obtain the daily
average absolute humidity.
Transmission Model
We used a
“susceptible–infectious–removed” model 5 with 2 age classes, persons aged 5
to 18 years (school-age children) and others. We allowed transmission within
and between age classes to vary for up to 4 different transmission parameters,
and we multiplied each transmission parameter by the same seasonal factor
(either a sinusoid or a function of temperature or absolute humidity). We
assumed that the epidemic corresponded to a stochastic realization of the
individual-based version of this model, and that the observed case reports were
generated by sampling from the epidemic. We used a negative binomial sampling
distribution for reports, to account for possible clustering 5. The Supplement contains our model equations.
Parameter Estimation
We
constructed maximum likelihood estimates for the model parameters and initial
conditions by using the iterated filtering method of Ionides and colleagues 5, implemented in the POMP package,
version 0.16-9 (http://pomp.r-forge.r-project.org),
written for the R statistical computing environment (R Foundation for
Statistical Computing, Vienna, Austria). The 5 provides parameter estimates. In
our simple model, the mean infectious period is equivalent to the generation
time of the disease. For dynamic purposes, this value should be compared with
the observed generation time of the disease, not the observed infectious period
5. The Supplement discusses the initial conditions.
Table.
Maximum
Likelihood Estimates for Parameters of the Best-Fit, 2-Age-Class Transmission
Model for the 2 Largest Cities in Alberta and the Province
Table.
Role of the Funding Source
Our study was
funded by the Canadian Institutes of Health Research, the Natural Sciences and
Engineering Research Council of Canada, and the Public Health Agency of Canada.
The funding sources played no role in the design, conduct, or analysis of our
study or in the decision to submit the manuscript for publication.
Results
Patterns of Confirmed pH1N1 in Alberta
Between 19
April 2009 and 2 January 2010, ProvLab conducted respiratory virus tests on
35 510 specimens, of which 6745 (19%) were positive for pH1N1. The top
panel of 5 shows the weekly numbers of
specimens tested for respiratory virus, specimens positive for pH1N1, and
specimens positive for any influenza virus. Restricted testing was implemented
on 30 October 2009; although vaccination for pH1N1 was available to the general
public beginning on 26 October 2009, this is unlikely to have substantially
affected incidence before 30 October. The surge of testing in May (before
substantial growth in cases of pH1N1) seems to have resulted from general
public concern about pH1N1 induced by media attention and the coincident
circulation of other viruses (such as rhinoviruses and coronaviruses) in April
and May. This disparity between tests conducted and confirmed cases of pH1N1
highlights the various factors that drive influenza testing patterns in
addition to influenza illness.
Figure 1.
Age structure
of laboratory-confirmed cases of pH1N1 in Alberta, Canada, in 2009.
Dates when
schools closed and opened are indicated in blue. Classes ended on different
dates for different levels of school: high school (grades 10 to 12) on 12 June,
middle school (grades 7 to 9) on 22 June, elementary school (kindergarten [K]
to grade 6) on 26 June, and junior kindergarten (JK) on 19 June; classes
began on 27 August 2009 in Calgary and on 31 August 2009 in the rest of the
province (Field Services, Alberta Ministry of Education. Personal
communication.). The dotted line in each panel indicates the start of
restricted testing on 30 October 2009 5. pH1N1 = pandemic H1N1 influenza. Top.
Aggregate weekly total number of specimens tested, specimens positive for pH1N1
(red), and specimens positive for any type of influenza A or B, by date
of specimen collection. The 2 highest peaks in the weekly totals, which are too
high to be seen in the graph, are 2162 on 3 May 2009 and 3600 on 1 November
2009. Middle. Confirmed cases of pH1N1 broken into 2 age classes,
school-age children (aged 5–18 y) and all others (children aged <5 y
and adults aged >18 y). Bottom. Intensity plot of date of sample
collection versus age of patient, with cumulative cases by age shown in the bar
plot on the right.
The middle
panel of 5 shows weekly confirmed cases of
pH1N1 in school-age children (aged 5 to 18 years) and in all other persons.
Arrows indicate the dates on which classes ended in schools of various levels
and the dates on which schools reopened (which were the same for all levels and
the same in all locations except Calgary).
The bottom
panel of 5 shows the daily pattern of pH1N1
case confirmations for each age; the bar plot on the right shows the cumulative
age distribution of cases, which is consistent with age distributions inferred
in other studies on the basis of hospitalizations 5 and serology 5. The dates on which classes ended
are indicated as a function of age, which yields the blue boundary near the
bottom left of the panel. Incidence dropped sharply when schools closed, which
is consistent with the hypothesis that school closure reduces the level of
contact among school-age children (and also with a short incubation period for
pH1N1 5,5,5). This decrease could also be explained
in part by changes in reporting.
The dates on
which schools reopened preceded the observable growth of the second wave of
cases by several weeks (5, bottom). As the second wave
grew, the highest density of confirmed cases was in school-age children
(indicated in 5 by the age structure during the
first 2 weeks of October). In fact, school-age children had the highest density
of confirmed cases except from late June to late September (and after the
implementation of restricted testing).
5 summarizes the spatiotemporal structure
of the epidemic, showing the distribution of confirmed cases across the
province (5, left) and the temporal
pattern of the epidemic (5, right) by latitude. Weekly
time series for the 2 largest cities, Calgary and Edmonton, are shown above the
latitudinal plot. The names and populations of major cities and towns are
indicated at their latitudes, and their positions are highlighted on the map.
By the third week of the epidemic in mid-May, cases had already been confirmed
in large regions of the province; substantial growth had not yet occurred
anywhere, so a spatially structured control strategy would probably not have
prevented the spread of influenza throughout the province. Exponential growth
of the first wave was evident first in Edmonton, from which some latitudinal
spread is apparent (as it is from several other major population centers). The
second wave became evident earliest in Calgary, perhaps because schools opened
4 days earlier in Calgary than in the rest of the province; however, the long
delay before substantial growth of the second wave makes this uncertain. Note
that a sudden drop in incidence is expected if transmission is suddenly reduced
in the middle of an epidemic, when incidence is high. In contrast, when
incidence is low, a gradual change is expected after a change in transmission
rate. When schools opened in late August 2009, incidence rates were extremely
low; a sudden increase in transmission rate can start an exponential increase
in cases, but this would take several weeks to be detectable at the population
level.
Figure 2.
Spatial
structure of laboratory-confirmed cases of pH1N1 in Alberta, Canada, in 2009.
pH1N1 =
pandemic H1N1 influenza. Bottom left. Cumulative incidence by location
(larger disks indicate more confirmed cases). Bottom right. Epidemic progression,
aggregated by latitude. The cities and towns labeled on the right (with their
population sizes) are also highlighted at their exact position in the left
panel. Top right. Weekly confirmed cases in Calgary and Edmonton.
Modeling pH1N1 Transmission in Alberta
To examine
how transmission rates (as opposed to incidence) changed over the course of the
epidemic, we used a simple epidemiologic model with 2 age classes, school-age
children (aged 5 to 18 years) and all others. We modeled seasonal changes in
influenza transmission by using a sinusoidal function 5 and a functional response to
weather variables (temperature or absolute humidity 5,5,5,5), and also considered the possibility of
abrupt changes in transmission in either or both of the age classes. Because
school-based public-health responses could have led to increased testing while
school was in session, we also constructed models in which reporting rate was
allowed to vary among age classes and change abruptly. We used a standard
particle-filtering algorithm 5,5,5 to estimate 95% CIs for each model's
parameters.
We fit our
models to the data from the 2 largest cities, Calgary and Edmonton, and to the
province, and conducted an extensive model selection analysis in each case on
the basis of 20 model variants (Supplement). In all cases, the best-fit model according to
the sample size–corrected Akaike information criterion (AIC) 5 was found when we allowed
transmission rate to be linked to temperature, with an abrupt change in
incidence in school-age children (but not the other age class) on school
opening and closing dates and an intensive testing period at the beginning of
the epidemic. The 5 lists maximum likelihood parameter
estimates and 95% CIs. Models that used absolute humidity instead of
temperature, or changes in reporting rate rather than (or in addition to)
transmission rate, did not fit as well (change in AIC for Calgary >7 or
>22, respectively). During the second wave of the epidemic, a large decrease
in temperature obviously correlated with a large increase in cases of pH1N1 influenza
(5), which suggests a substantial
causative link; however, the exponential increase of the second wave began
before the substantial change in temperature, which indicates that the opening
of schools was probably a more important factor in seeding the second wave.
The 5 indicates that the predicted
magnitude of the reduction in transmission rate in school-age children was 63%
(95% CI, 43% to 84%) in Calgary, 100% (CI, 69% to 100%) in Edmonton, and 86%
(CI, 70% to 100%) in Alberta. Our estimates of the aggregate basic reproductive
number are consistent with analyses of other pH1N1 data 5,5,5,5.
To study the
link between the observed change in transmission and the school schedule, we
refitted our model while allowing the dates of transmission change to be free
parameters (Supplement). We found that the 95% CIs for the estimated
dates on which the transmission rate decreased in school-age children are
narrow and overlap (or nearly overlap, in the case of Edmonton) with the range
of dates when schools actually closed (5). The 95% CIs for the estimated
dates on which the transmission rate increased in this age class are much
wider; much greater uncertainty is expected when estimating this date because
stochastic variations are relatively more important at the start than in the
middle of an outbreak. After Calgary and Edmonton, the next largest city in
Alberta (Red Deer) is smaller by an order of magnitude, and the data during the
first wave were very noisy (5), which makes it difficult to
detect the beginning and end of the wave, as well as any relationships with the
school calendar or weather patterns. We therefore restricted our analyses to
the 2 largest cities and to the province.
Predicted Outcome If Schools Had Not Been Closed
5 compares simulation time series with the
observed pH1N1 incidence data for Alberta as a whole; Supplement Figures 1 and 2 compare these data for Calgary
and Edmonton, respectively. In each figure, the simulations used for the top
panels are based on the parameters estimated for our best-fit model (5), whereas the bottom panels show
what the same model predicts if schools had remained open all summer: The first
wave would not have burnt out but would still have been moderated by temperature
effects; more persons would have been infected before the vaccine became
available; and a major second wave induced by temperature effects would still
have occurred in the fall. The predicted factor by which the total number of
cases would have been greater if schools had remained open is 1.38 (CI, 1.21 to
1.64) in Calgary, 1.54 (CI, 1.36 to 1.77) in Edmonton, and 2.1 (CI, 2.0 to 2.5)
in the province. Of note, although our best-fit models include the effects of
temperature, our conclusions do not depend specifically on including
temperature. Including absolute humidity instead yields lower AICs but similar
parameter estimates and results (in particular, a similar estimate for the
effect of school closure on transmission and on the incidence pattern in the
absence of school closure). Temperature variations could coincidentally yield
the best AIC among the seasonal models; the key point with respect to
seasonality is that we have strong evidence for a seasonal effect on
transmission (with no seasonal forcing, change in AIC compared with the
best-fit model was >14 for Calgary and >31 for Edmonton). Ignoring school
closure also precludes a good fit (change in AIC >22 for Calgary and >23
for Edmonton).
Figure 3.
Comparison of
pH1N1 data for the province of Alberta with simulations.
Box plots are
based on 1000 realizations of our best-fit model, as specified in the 5. Data and simulation results are
shown for school-age children (aged 5–18 y) (left panels) and for the
rest of the population (right panels). Data are compared with
simulations of our best-fit model (5) (top panels) and with
predicted results if schools had been left open in Alberta throughout the
summer (bottom panels). pH1N1 = pandemic H1N1 influenza.
Discussion
Much previous
research 5,5,5,5,5,5,5,5,5 has aimed to connect observed temporal
patterns of influenza epidemics with unobserved changes in transmission rate
and to connect inferred changes in transmission rate with observed or inferred
changes in environmental conditions or human behavior. This previous work has
shown that convincingly establishing such links is difficult at best.
Our findings
strongly indicate a large reduction in influenza transmission resulting from
schools closing for the summer. Although our models cannot include all relevant
factors, we have shown that this result is robust to a wide range of
assumptions and holds up whether we consider the whole province of Alberta or
look separately at large cities. In particular, the result is robust even when
we explore different assumptions about influenza reporting.
Given the
correlation between the drop in incidence in school-age children and the dates
when classes ended, as well as the abrupt associated change in transmission
that our models identify, we infer that school closure vastly reduced
transmission in school-age children, which substantially reduced the incidence
of influenza (initially in school-age children and within a few weeks in the
entire population). Our modeling also points to a dramatic increase in
transmission among school-age children after schools opened.
Closing
schools in Alberta was not undertaken as a control measure; the first wave of
pH1N1 infection happened to occur when classes ended for the summer. However,
our observations suggest that closing all schools could affect the course of
future epidemics, regardless of when they occur. Of course, policymakers would
also need to consider the social disruption that would result from closing all
schools in such a large area as Alberta during the normal school year.
The key
inference of our study is that school-age children were fundamentally important
drivers of pH1N1 transmission in 2009. Systematically reducing transmission in
this age group could substantially mitigate the effects of future pandemics. We
suggest that school closures (either local or regional) should be seriously
considered if a pandemic occurs during the school year. Our findings also
support targeting schoolchildren for interventions aimed at interrupting
influenza transmission, including vaccination 5, hygiene 5,5, and chemoprophylaxis.
Our modeling
also indicated that seasonal changes in weather (such as changes in temperature
or humidity) significantly affected influenza transmission in cities in
Alberta. Although temperature fits these particular data substantially better
than humidity, the fits yield similar parameter estimates, and we consider both
measures as proxies for more complex seasonal and weather effects. In places
where summer started earlier than in Alberta, it would not be surprising to
find that the decline of the first wave of the 2009 H1N1 influenza pandemic
began before schools closed for the summer.
Finally, our
work shows the value of unrestricted virologic testing. Data like those we have
analyzed greatly increase our power to discover the cause of sudden changes in
incidence, whether they result from school closures or other factors. Our
approach (comparing the performance of many simple models fitted to high-volume
data) is generally underutilized in settings of infectious disease outbreaks.
In the future, if data were made available in real time for this type of
analysis, debates over the key drivers of incidence could be helpfully
constrained.
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