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The authors have declared that no competing interests exist.

Conceived and designed the experiments: CJ EV PM. Performed the experiments: CJ. Analyzed the data: CJ. Contributed reagents/materials/analysis tools: CJ EV. Wrote the paper: CJ EV PM PF.

Current address: Research Department of Infection and Population Health, University College London, London, United Kingdom

Changes in children’s contact patterns between termtime and school holidays affect the transmission of several respiratory-spread infections. Transmission of varicella zoster virus (VZV), the causative agent of chickenpox, has also been linked to the school calendar in several settings, but temporal changes in the proportion of young children attending childcare centres may have influenced this relationship.

We used two modelling methods (a simple difference equations model and a Time series Susceptible Infectious Recovered (TSIR) model) to estimate fortnightly values of a contact parameter (the per capita rate of effective contact between two specific individuals), using GP consultation data for chickenpox in England and Wales from 1967–2008.

The estimated contact parameters were 22–31% lower during the summer holiday than during termtime. The relationship between the contact parameter and the school calendar did not change markedly over the years analysed.

In England and Wales, reductions in contact between children during the school summer holiday lead to a reduction in the transmission of VZV. These estimates are relevant for predicting how closing schools and nurseries may affect an outbreak of an emerging respiratory-spread pathogen.

Chickenpox is caused by varicella zoster virus (VZV), which is spread primarily by the respiratory route. In temperate regions, almost all individuals become infected with VZV during their lifetime, usually during childhood ^{th} Century Denmark

Since the mid 1980s, the age distribution of GP (primary care) consultations for chickenpox in England and Wales has changed, with an increasing proportion of cases being aged <5 years and a decreasing proportion being aged 5–14 years

In this paper, we apply two modelling approaches to long-term data (from 1967–2008) from England and Wales to estimate how the rate of VZV transmission changes during the year and whether its relationship to school holidays has changed over time. We calculate fortnightly values of a contact parameter, defined as the per capita rate of effective contact (i.e. contact sufficient to allow transmission) between two specific individuals

The Royal College of General Practitioners (RCGP) Research and Surveillance Centre runs a sentinel primary care (GP) surveillance scheme in England and Wales

Fortnightly birth rates per 100,000, for 1967–2008, were estimated by dividing the annual number of births (available from the UK Office for National Statistics

In England and Wales, school holiday dates are set locally by 326 Local Authority Districts (LADs). School holiday dates were identified from the websites of three randomly selected LADs from each of nine geographical regions

We used two approaches to explore how the rate of effective contact differs between termtime and holidays. Firstly, we used a simple mass action model, based on one used by Fine and Clarkson _{t}_{t}_{t}

We used an approach from TSIR modelling to estimate the reporting fraction (the percentage of infections that are reported to the surveillance system) for both the simple mass action model and the TSIR model.

To estimate the reporting fraction (_{t}_{t} = S_{t}−

As the age distribution of chickenpox consultations changed over time

We used a modification of the method used by Fine and Clarkson _{t}

The values of _{t}_{t+1}

The TSIR model

The contact parameter _{t}_{t}_{t} = _{t}_{t}

This regression was fitted separately for the periods 1967–76, 1977–97 and 1998–2008. In each regression, variations in _{t}_{t}_{t}_{t}_{t}

In sensitivity analyses we repeated the analyses after fixing the parameter

We assessed the consistency between predictions based on the estimated values of _{t}_{t}_{t}

For the estimates from the simple mass action and TSIR models, the percentage difference between _{t}_{term}–_{holiday})/_{term}), where

All analyses were carried out in Stata, version 12.

From 1967–2008, chickenpox consultation rates were highest in 0–4 and 5–14 year-olds (Figure S1 in

The contact parameter estimated using the simple mass action model was in general lowest during the summer holiday, but seasonal patterns differed between years (

The proportion susceptible at the start of the time series was assumed to be 13%; shading shows approximate timing of school holidays.

Estimates are based on the simple mass action model. Error bars show 95% confidence intervals.

Estimates from the simple mass action model of the percentage difference between the contact parameter between termtime and school holiday were insensitive to the assumed number of susceptible individuals in 1967 and the dates of school holidays (Figures S10-12 in

The estimated reporting fraction was highest during 1977–98 (42.8%, 95% CI 42.7–42.9%), compared to 29.6% (95% CI 29.3–29.9%) and 31.6% (95% CI 31.4–31.8%) in 1967–76 and 1998–2008, respectively (Figure S2 in

Analyses of the RCGP data for the periods 1967–76, 1977–97 and 1998–2008, using Equation 5, suggested that on average 9% (95% CI 2–100%), 11% (95% CI 2–100%) and 18% (95% CI 1–100)%, respectively, of the population was susceptible to VZV, although the CIs were very wide. The corresponding estimates of

Estimates of the contact parameter decreased over time, ranging from 2.25×10^{−4} to 4.71×10^{−4} per fortnight in 1967–76, 2.00×10^{−4} to 4.00×^{−4} per fortnight in 1977–97, and 1.15×10^{−4} to 2.30×10^{−4} per fortnight in 1998–2008 (

A) 1967–76; B) 1977–97; C) 1998–2008; with values of α as shown. Error bars show 95% confidence intervals. Shaded rectangles show the approximate timing of school holidays. Fortnight 1 is the first two weeks of January; fortnight 26 is the last two weeks of December.

A) all school holidays; B) summer holidays, with different values of α. A positive value represents a reduction in the contact parameter during holidays.

The fitted values of the number of chickenpox cases from the regression (scaled down for under-reporting) compared well with the observed RCGP data: the correlation coefficient was 0.929 (95% CI 0.920–0.937,

A) Relationship between the RCGP chickenpox consultation rates and the fitted values from the regression (scaled down for under-reporting); B) RCGP data and the values predicted by the difference equations using the estimated contact parameters.

We estimate that contact between children sufficient for transmission of chickenpox is 22

We used a long, contemporary time series to analyse the effects of school holidays on contact patterns, taking into account temporal changes in the reporting fraction. However, the comparisons of the contact parameter between termtime and holidays have some limitations. They do not account for other seasonal factors, such as weather, which might affect transmission (particularly temperature: several studies have found the highest incidence of chickenpox to occur in the coolest months of the year)

We did not formally assess the effects of the Christmas and Easter holidays on contact patterns, for several reasons. Firstly, consultation behaviour over the Christmas and New Year periods will differ from that during the rest of the year. Secondly, the Christmas holiday lasts only two weeks, meaning that any comparison of the _{t}

The TSIR and simple mass action models are based on the same principles, and produced similar point estimates of the effects of school holidays on the transmission of VZV. The TSIR model is statistically rigorous, e.g. it easily allows calculation of confidence intervals for the weekly estimates of the contact parameter. However, it assumes that the annual pattern in the contact parameter (and therefore the effect of school holidays) is the same in all years. Our implementation of the simple mass action model allowed the seasonal pattern to differ between years but does not indicate the precision of the estimates of the fortnightly contact parameters. The absence of a clear trend in the effects of school holidays on the contact parameter as estimated using the simple mass action model therefore supports the conclusion from the TSIR model that there was no systematic change in the effects of school holidays over time.

Our results are consistent with previous studies of chickenpox. Monthly estimates of the contact parameter in New York City (1931

Monthly estimates of the basic reproduction number (R_{0}, the average number of secondary infectious cases resulting from a single infectious person introduced into a completely susceptible population) for chickenpox, from a TSIR model applied to data from early 20^{th} Century Copenhagen, also appeared lowest during the summer holiday _{0} was ∼11

Previous studies have suggested that the contact parameter for chickenpox between school-aged children has increased over time _{t}

The average percentage of the population that is susceptible to chickenpox was estimated as 9%, 11% and 20% during 1967

The seasonal pattern in the contact parameter was independent of the assumed proportion susceptible at the start of each time period, and remained consistent over time despite changes in preschool childcare attendance. This may be because preschool centres often (although not always) close over summer

Our estimates of the reporting fraction (approximately 30%, 43% and 32% for 1967

An alternative method of estimating the reporting fraction involves comparing age-specific serological data with the cumulative proportion of a birth cohort reported to have had the infection by a given age, as done for measles

Contact surveys (in which participants report the number of individuals with whom they make contact)

Transmission of other viral infections spread by the respiratory route, including measles

School closures, with or without concurrent closure of nurseries, may be considered as an outbreak control measure

(DOCX)

We thank Michele Barley (RCGP Research and Surveillance Centre) for providing the consultation data. We also thank Ben Armstrong, Jessica Metcalf and Ottar Bjornstad for helpful discussions. Historical term dates were taken from correspondence between Paul Fine and the Inner London Education Authority dating from the 1980s.