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Original Research |

Effects of School Closure on Incidence of Pandemic Influenza in Alberta, Canada FREE

David J.D. Earn, PhD; Daihai He, PhD; Mark B. Loeb, MD, MSc; Kevin Fonseca, PhD; Bonita E. Lee, MD, MSc; and Jonathan Dushoff, PhD
[+] Article and Author Information

From McMaster University, Hamilton, Ontario; University of Calgary, Calgary, Alberta; and Edmonton Clinic Health Academy, Edmonton, Alberta, Canada.


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.


Ann Intern Med. 2012;156(3):173-181. doi:10.7326/0003-4819-156-3-201202070-00005
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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: 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.

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.

Conclusion: 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.

Primary Funding Source: Canadian Institutes of Health Research, Natural Sciences and Engineering Research Council of Canada, and Public Health Agency of Canada.

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 (1), and school closure is one of the most frequently considered measures (2). Influenza incidence and mortality data do not typically show obvious effects of school closures, but several studies (24) 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 (6). The subtype of the new virus (A/H1N1) was the same as the 1918 pandemic strain, descendants of which have circulated continuously since 1977 (7). 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 (8). The World Health Organization declared the outbreak to be a pandemic on 11 June 2009 (8). 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 (910). 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 (11). 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 [12]), 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 (1317), 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 (1820). 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.

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) (21). We obtained testing data by using the Data Integration for Alberta Laboratories application (22), 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 (23) 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 (24). 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 (25), 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 Table 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 (26). The Supplement discusses the initial conditions.

Table Jump PlaceholderTable.  Maximum Likelihood Estimates for Parameters of the Best-Fit, 2-Age-Class Transmission Model for the 2 Largest Cities in Alberta and the Province
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.

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 Figure 1 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.

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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 (12). 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.

Grahic Jump Location

The middle panel of Figure 1 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 Figure 1 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 (27) and serology (28). 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 [16, 2930]). 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 (Figure 1, bottom). As the second wave grew, the highest density of confirmed cases was in school-age children (indicated in Figure 1 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).

Figure 2 summarizes the spatiotemporal structure of the epidemic, showing the distribution of confirmed cases across the province (Figure 2, left) and the temporal pattern of the epidemic (Figure 2, 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.

Grahic Jump Location
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.

Grahic Jump Location
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 (31) and a functional response to weather variables (temperature or absolute humidity [3235]), 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 (24, 3637) 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) (38) 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 Table 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 (Figure 1), 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 Table 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 (1316).

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 (Figure 2). 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 (Figure 2), 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

Figure 3 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 (Table), 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).

Grahic Jump Location
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 Table. 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 (Table) (top panels) and with predicted results if schools had been left open in Alberta throughout the summer (bottom panels). pH1N1 = pandemic H1N1 influenza.

Grahic Jump Location

Much previous research (25, 1820, 3940) 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 (41), hygiene (4243), 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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Lowen AC, Mubareka S, Steel J, Palese P.  Influenza virus transmission is dependent on relative humidity and temperature. PLoS Pathog. 2007; 3:1470-6. PubMed
CrossRef
 
Shaman J, Kohn M.  Absolute humidity modulates influenza survival, transmission, and seasonality. Proc Natl Acad Sci U S A. 2009; 106:3243-8. PubMed
CrossRef
 
Shaman J, Pitzer V, Viboud C, Lipsitch M, Grenfell B.  Absolute humidity and the seasonal onset of influenza in the continental US. PLoS Curr. 2009; 1:RRN1138. PubMed
CrossRef
 
Makoto S, Kouki K, Kunio S.  Absolute humidity as a deterministic factor affecting seasonal influenza epidemics in Japan. Tohoku J Exp Med. 2011; 224:251-256.
CrossRef
 
Doucet A, De Fritas N, Gordon N.  Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science. New York: Springer; 2001.
 
He D, Ionides EL, King AA.  Plug-and-play inference for disease dynamics: measles in large and small populations as a case study. J R Soc Interface. 2010; 7:271-83. PubMed
CrossRef
 
Burnham KP, Anderson DR.  Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. New York: Springer; 2002.
 
Earn DJ, Dushoff J, Levin SA.  Ecology and evolution of the flu. Trends in Ecology and Evolution. 2002; 17:334-40.
CrossRef
 
Dushoff J, Plotkin JB, Levin SA, Earn DJ.  Dynamical resonance can account for seasonality of influenza epidemics. Proc Natl Acad Sci U S A. 2004; 101:16915-6. PubMed
CrossRef
 
Loeb M, Russell ML, Moss L, Fonseca K, Fox J, Earn DJ. et al.  Effect of influenza vaccination of children on infection rates in Hutterite communities: a randomized trial. JAMA. 2010; 303:943-50. PubMed
CrossRef
 
Aiello AE, Murray GF, Perez V, Coulborn RM, Davis BM, Uddin M. et al.  Mask use, hand hygiene, and seasonal influenza-like illness among young adults: a randomized intervention trial. J Infect Dis. 2010; 201:491-8. PubMed
CrossRef
 
Aiello AE, Coulborn RM, Aragon TJ, Baker MG, Burrus BB, Cowling BJ. et al.  Research findings from nonpharmaceutical intervention studies for pandemic influenza and current gaps in the research. Am J Infect Control. 2010; 38:251-8. PubMed
CrossRef
 
Gillespie DT.  A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Computational Physics. 1976; 22:403-34.
CrossRef
 
Earn DJ.  Mathematical epidemiology of infectious diseases. Lewis MA, Chaplain MA, Keener JP, Maini PK Mathematical Biology. IAS/Park City Mathematics Series. vol 14. Providence, RI: American Mathematical Soc; 2009; 151-86.
 
Campbell GS, Norman JM.  An Introduction to Environmental Biophysics. 2nd ed. New York: Springer-Verlag; 1998.
 
Pulinets SA, Ouzounov D, Ciraolo L, Singh R, Cervone G, Leyva A. et al.  Thermal, atmospheric and ionospheric anomalies around the time of the Colima M7.8 earthquake of 21 January 2003. Annales Geophysicae. 2006; 24:835-49.
CrossRef
 
Government of Alberta.  2006 Census Analysis: Alberta Profile. Edmonton, Alberta, Canada: Alberta Employment & Immigration; 2009. Accessed at www.employment.alberta.ca/documents/LMI/LMI-CA_alberta_profile.pdf on 21 November 2011.
 
Ma J, Ma Z.  Epidemic threshold conditions for seasonally forced seir models. Math Biosci Eng. 2006; 3:161-72. PubMed
CrossRef
 
Akaike H.  A new look at the statistical model identification. IEE Trans Autom Control. 1974; 19:716-23.
CrossRef
 
King AA, Ionides EL, Pascual M, Bouma MJ.  Inapparent infections and cholera dynamics. Nature. 2008; 454:877-80. PubMed
CrossRef
 

Figures

Grahic Jump Location
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 (12). 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.

Grahic Jump Location
Grahic Jump Location
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.

Grahic Jump Location
Grahic Jump Location
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 Table. 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 (Table) (top panels) and with predicted results if schools had been left open in Alberta throughout the summer (bottom panels). pH1N1 = pandemic H1N1 influenza.

Grahic Jump Location

Tables

Table Jump PlaceholderTable.  Maximum Likelihood Estimates for Parameters of the Best-Fit, 2-Age-Class Transmission Model for the 2 Largest Cities in Alberta and the Province

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Ghani AC, Baguelin M, Griffin J, Flasche S, Pebody R, van Hoek AJ. et al.  The early transmission dynamics of H1N1pdm influenza in the United Kingdom. PLoS Curr. 2009; 1:RRN1130. PubMed
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Moser MR, Bender TR, Margolis HS, Noble GR, Kendal AP, Ritter DG.  An outbreak of influenza aboard a commercial airliner. Am J Epidemiol. 1979; 110:1-6. PubMed
 
London WP, Yorke JA.  Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. Am J Epidemiol. 1973; 98:453-68. PubMed
 
Lowen AC, Mubareka S, Steel J, Palese P.  Influenza virus transmission is dependent on relative humidity and temperature. PLoS Pathog. 2007; 3:1470-6. PubMed
CrossRef
 
Shaman J, Kohn M.  Absolute humidity modulates influenza survival, transmission, and seasonality. Proc Natl Acad Sci U S A. 2009; 106:3243-8. PubMed
CrossRef
 
Shaman J, Pitzer V, Viboud C, Lipsitch M, Grenfell B.  Absolute humidity and the seasonal onset of influenza in the continental US. PLoS Curr. 2009; 1:RRN1138. PubMed
CrossRef
 
Makoto S, Kouki K, Kunio S.  Absolute humidity as a deterministic factor affecting seasonal influenza epidemics in Japan. Tohoku J Exp Med. 2011; 224:251-256.
CrossRef
 
Doucet A, De Fritas N, Gordon N.  Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science. New York: Springer; 2001.
 
He D, Ionides EL, King AA.  Plug-and-play inference for disease dynamics: measles in large and small populations as a case study. J R Soc Interface. 2010; 7:271-83. PubMed
CrossRef
 
Burnham KP, Anderson DR.  Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. New York: Springer; 2002.
 
Earn DJ, Dushoff J, Levin SA.  Ecology and evolution of the flu. Trends in Ecology and Evolution. 2002; 17:334-40.
CrossRef
 
Dushoff J, Plotkin JB, Levin SA, Earn DJ.  Dynamical resonance can account for seasonality of influenza epidemics. Proc Natl Acad Sci U S A. 2004; 101:16915-6. PubMed
CrossRef
 
Loeb M, Russell ML, Moss L, Fonseca K, Fox J, Earn DJ. et al.  Effect of influenza vaccination of children on infection rates in Hutterite communities: a randomized trial. JAMA. 2010; 303:943-50. PubMed
CrossRef
 
Aiello AE, Murray GF, Perez V, Coulborn RM, Davis BM, Uddin M. et al.  Mask use, hand hygiene, and seasonal influenza-like illness among young adults: a randomized intervention trial. J Infect Dis. 2010; 201:491-8. PubMed
CrossRef
 
Aiello AE, Coulborn RM, Aragon TJ, Baker MG, Burrus BB, Cowling BJ. et al.  Research findings from nonpharmaceutical intervention studies for pandemic influenza and current gaps in the research. Am J Infect Control. 2010; 38:251-8. PubMed
CrossRef
 
Gillespie DT.  A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Computational Physics. 1976; 22:403-34.
CrossRef
 
Earn DJ.  Mathematical epidemiology of infectious diseases. Lewis MA, Chaplain MA, Keener JP, Maini PK Mathematical Biology. IAS/Park City Mathematics Series. vol 14. Providence, RI: American Mathematical Soc; 2009; 151-86.
 
Campbell GS, Norman JM.  An Introduction to Environmental Biophysics. 2nd ed. New York: Springer-Verlag; 1998.
 
Pulinets SA, Ouzounov D, Ciraolo L, Singh R, Cervone G, Leyva A. et al.  Thermal, atmospheric and ionospheric anomalies around the time of the Colima M7.8 earthquake of 21 January 2003. Annales Geophysicae. 2006; 24:835-49.
CrossRef
 
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Ma J, Ma Z.  Epidemic threshold conditions for seasonally forced seir models. Math Biosci Eng. 2006; 3:161-72. PubMed
CrossRef
 
Akaike H.  A new look at the statistical model identification. IEE Trans Autom Control. 1974; 19:716-23.
CrossRef
 
King AA, Ionides EL, Pascual M, Bouma MJ.  Inapparent infections and cholera dynamics. Nature. 2008; 454:877-80. PubMed
CrossRef
 

Letters

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

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School Session Status and the 2009 H1N1 Pandemic
Posted on February 13, 2012
Olivia R., Briffault, Student
Hunter College High School
Conflict of Interest: None Declared

The results of this (Earn et al) paper confirm the results of earlier studies that exploited the substantial variation in school summer vacation dates across the United States. Chao et al. 2010 examined the relationship between H1N1 and the end of school summer vacation in the US and finds influenza rates were significantly higher after schools reopened in the fall. In a similar study, I found that influenza rates are about 1.7 times higher when children were in school than when they were not. The results were stronger for school closing in the spring than school reopening in the fall.

References

Chao DL, Halloran ME, Longini IM, Jr. School opening dates predict pandemic influenza A(H1N1) outbreaks in the United States. J Infect Dis 2010;202(6):877-80.

Briffault, Olivia. Weekly influenza-like-Illness rates were significantly lower in areas where schools were not in session in the United States during the 2009 H1N1 pandemic [Internet]. Version 14. PLoS Currents: Influenza. 2011 Mar 27 [revised 2011 Apr 27]:PMC3091530.

Conflict of Interest:

None declared

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Supplements

Supplemental Content
Data Supplement

Summary for Patients

Effects of School Closure on Incidence of Pandemic Influenza in Alberta, Canada

The full report is titled “Effects of School Closure on Incidence of Pandemic Influenza in Alberta, Canada.” It is in the 7 February 2012 issue of Annals of Internal Medicine (volume 156, pages 173-181). The authors are D.J.D. Earn, D. He, M.B. Loeb, K. Fonseca, B.E. Lee, and J. Dushoff.

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