The impact of regular school closure on seasonal influenza epidemics: a data-driven spatial transmission model for Belgium

Abstract

Background: School closure is often considered as an option to mitigate influenza epidemics because of its potential to reduce transmission in children and then in the community. The policy is still however highly debated because of controversial evidence. Moreover, the specific mechanisms leading to mitigation are not clearly identified.

Methods: We introduced a stochastic spatial age-specific metapopulation model to assess the role of holiday-associated behavioral changes and how they affect seasonal influenza dynamics. The model is applied to Belgium, parameterized with country-specific data on social mixing and travel, and calibrated to the 2008/2009 influenza season. It includes behavioral changes occurring during weekend vs. weekday, and holiday vs. school-term. Several experimental scenarios are explored to identify the relevant social and behavioral mechanisms.

Results: Stochastic numerical simulations show that holidays considerably delay the peak of the season and mitigate its impact. Changes in mixing patterns are responsible for the observed effects, whereas changes in travel behavior do not alter the epidemic. Weekends are important in slowing down the season by periodically dampening transmission. Christmas holidays have the largest impact on the epidemic, however later school breaks may help in reducing the epidemic size, stressing the importance of considering the full calendar. An extension of the Christmas holiday of 1 week may further mitigate the epidemic.

Conclusion: Changes in the way individuals establish contacts during holidays are the key ingredient explaining the mitigating effect of regular school closure. Our findings highlight the need to quantify these changes in different demographic and epidemic contexts in order to provide accurate and reliable evaluations of closure effectiveness. They also suggest strategic policies in the distribution of holiday periods to minimize the epidemic impact.

Keywords: Epidemic modeling; Influenza; Metapopulation; School closure; Spatial transmission.

Fig. 1

Schematic illustration of the spatial age-structured metapopulation model. The metapopulation modeling scheme is composed of three layers. At the country scale, Belgium is modeled as a set of patches (here indicated with q and p) corresponding to municipalities coupled through mobility of individuals f_pq(i) of age class i at time t. Within each municipality, population is divided into two age classes, children (c) and adults (a), whose mixing pattern is defined by the contact matrix C. Individuals resident of patch p and individuals commuting to that patch (e.g. resident of patch q) mix together following commuting. The figure reports as an example the contact matrix of a regular weekday (Eq. (3)). Mobility and mixing vary based on the calendar day (regular/holiday, weekday/weekend). Influenza disease progression at the individual level is modeled through a Susceptible-Exposed-Infectious-Recovered compartmental scheme, with β indicating the per-contact transmission rate, ε the rate from exposed to infectious state, μ the recovery rate

Fig. 2

Calibration results. (a)-(b): Simulated and empirical incidence curves for the district of Brussels (panel a) and for the entire Belgium (panel b). The incidence curve of Brussels is the sole empirical data used for the calibration of the model. Different vertical axes referring to empirical (black curve, left axis) vs. simulated (red curve, right axis) incidences are used for the sake of comparison of the two curves. Different incidence values are due to unknown GP consultation rates characterising ILI surveillance data. (c)-(f): Probability distribution of the values of the reproductive number R^p computed in each patch following the calibration. They refer to the different day types explored, i.e. belonging to a regular weekday (panel c), regular weekend (d), holiday weekday (e), holiday weekend (f)

Fig. 3

Role of social mixing vs. travel behavior. (a): Simulated weekly incidence profiles for influenza in Belgium. The realistic model is compared to the travel changes model, the mixing changes model, the regular weekday model. Median curves are shown for all cases, along with 50% confidence intervals (dark shade) and 95% CI (light shade), for the realistic and regular weekday model (they are not shown for the other models for the sake of visualization). (b)-(c)-(d): Peak time difference $\left(\Delta T^p=T_{\mathit{\text{scenario}}}^p-T_{\mathit{\text{realistic}}\text{model}}^p\right)$, relative variation of epidemic size $\left(\Delta {\sigma }^p=\left({\sigma }_{\mathit{\text{scenario}}}^p-{\sigma }_{\mathit{\text{realistic}}\text{model}}^p\right)/{\sigma }_{\mathit{\text{realistic}}\text{model}}^p\right)$, and relative variation of peak incidence $\left(\Delta I^p=\left(I_{\mathit{\text{scenario}}}^p-I_{\mathit{\text{realistic}}\text{model}}^p\right)/I_{\mathit{\text{realistic}}\text{model}}^p\right)$, respectively, across the three experimental scenarios (see “Methods” for more details). Boxplots refer to the distributions across patches

Fig. 4

Impact of school holiday periods and holiday extensions. (a)-(b)-(c): Peak time difference, relative variation of epidemic size, and relative variation of peak incidence, respectively, across the following experimental scenarios: w/o Fall holiday model, w/o Christmas holiday model, w/o Winter holiday model, w/o Easter holiday model, w/o holiday model. Boxplots refer to the distributions across patches. (d)-(e)-(f): Peak time difference, relative variation of epidemic size, and relative variation of peak incidence, respectively, for the Christmas holiday extension models, before or after the break. Boxplots refer to the distributions across patches

Fig. 5

Effect of epidemic timing. (a): Simulated weekly incidence profiles for influenza in Belgium. The realistic model is compared to the scenarios considering the anticipation or delay of the epidemic (− 4w model, − 2w model, + 2w model, + 4w model). Median curves are shown along with 95% CI (light shade). (b)-(c)-(d): Peak time difference, relative variation of epidemic size and relative variation of peak incidence, respectively, across the considered experimental scenarios. Boxplots refer to the distributions across patches. The peak time difference ΔT^p discounts the time shift of the initial conditions of the considered model