key: cord-0886950-pgze0v2l
authors: Rozhnova, G.; van Dorp, C. H.; Bruijning-Verhagen, P.; Bootsma, M. C. J.; van de Wijgert, J. H. H. M.; Bonten, M. J. M.; Kretzschmar, M. E.
title: Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic
date: 2020-12-08
journal: nan
DOI: 10.1101/2020.12.07.20245506
sha: 50cde2e9e03190453f458b5f26bbcecb9e86ce12
doc_id: 886950
cord_uid: pgze0v2l

Background: In autumn 2020, many countries, including the Netherlands, are experiencing a second wave of the COVID-19 pandemic. Health policymakers are struggling with choosing the right mix of measures to keep the COVID-19 case numbers under control, but still allow a minimum of social and economic activity. The priority to keep schools open is high, but the role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We used a transmission model to estimate the impact of school contacts on the transmission of SARS-CoV-2 and to assess the effects of school-based measures, including school closure, on controlling the pandemic at different time points during the pandemic. Methods and Findings: The age-structured model was fitted to age-specific seroprevalence and hospital admission data from the Netherlands during spring 2020. Compared to adults older than 60 years, the estimated susceptibility was 23% (95%CrI 20-28%) for children aged 0 to 20 years and 61% (95%CrI 50%-72%) for the age group of 20 to 60 years. The time points considered in the analyses were (i) August 2020 when the effective reproduction number (R_e) was estimated to be 1.31 (95%CrI 1.15-2.07), schools just opened after the summer holidays and measures were reinforced with the aim to reduce R_e to a value below 1, and (ii) November 2020 when measures had reduced R_e to 1.00 (95%CrI 0.94-1.33). In this period schools remained open. Our model predicts that keeping schools closed after the summer holidays, in the absence of other measures, would have reduced R_e by 10% (from 1.31 to 1.18 (95%CrI 1.04-1.83)) and thus would not have prevented the second wave in autumn 2020. Reducing non-school-based contacts in August 2020 to the level observed during the first wave of the pandemic would have reduced R_e to 0.83 (95%CrI 0.75-1.10). Yet, this reduction was not achieved and the observed R_e in November was 1.00. Our model predicts that closing schools in November 2020 could reduce R_e from the observed value of 1.00 to 0.84 (95%CrI 0.81-0.90), with unchanged non-school based contacts. Reductions in R_e due to closing schools in November 2020 were 8% for 10 to 20 years old children, 5% for 5 to 10 years old children and negligible for 0 to 5 years old children. Conclusions: The impact of measures reducing school-based contacts, including school closure, depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce R_e with non-school-based measures are exhausted or undesired and R_e is still close to 1, the additional benefit of school-based measures may be considerable, particularly among the older school children.

In autumn 2020, many countries, including the Netherlands, are experiencing a second wave of the COVID-19 29 pandemic [1] . During the first wave in spring 2020, general population-based control physical distancing measures 30 were introduced in the Netherlands, which included refraining from hand-shaking, work from home if possible, self-31 isolation of persons with cold-or flu-like symptoms and closure of all schools. These contact-reduction measures 32 were relaxed starting from May, and the incidence of COVID-19 started to increase again at the end of July [1] . where k = 1, . . . , n, become latently infected (E k ) via contact with infectious persons in m infectious stages (I k,p , p = 1, . . . , m) at a rate β k λ k , where λ k is the force of infection, and β k is the reduction in susceptibility to infection of persons in age group k compared to persons in age group n. Exposed persons (E k ) become infectious (I k,1 ) at rate α. Infectious persons progress through (m − 1) infectious stages at rate γm, after which they recover (R k ). From each stage, infectious persons are hospitalized at rate ν k . Table 1 gives the summary of the model parameters. (B)-(D) Contact rates. (B) and (C) show contact rates in all locations before the pandemic and after the first lockdown (April 2020), respectively. (D) shows contact rates at schools before the pandemic. The color represents the average number of contacts a person in a given age group had with persons in another age group.

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The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint 116 where the contribution of the contact rate after the first lockdown is given by the logistic function 117 f (t) = 1 1 + e −K1(t−t1)

(2) 118 with the mid-point value t 1 and the logistic growth K 1 . The parameter K 1 governs the speed at which control 119 measures are rolled out, and t 1 is the mid-time point of the lockdown period ( Figure S1 ). The special cases of 125 where g(t) = 1/ 1 + e K2(t−t2) with the mid-point value t 2 > t 1 and the logistic growth K 2 . In Eq. 3, the first two 126 terms describe the increase of non-school contacts from the level after the first lockdown to their pre-lockdown level.

The parameter ζ 2 ≥ ζ 1 , 0 ≤ ζ 2 ≤ 1 implies that the probability of transmission increased due to reduced adherence 128 to control measures. The last term describes opening of schools which we assume to happen instantaneously, where 129 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint s kl denotes the school contact rate at the pre-lockdown level (Figure 1 D) , and ω, 0 ≤ ω ≤ 1 is the proportion 130 of retained school contacts. Schools functioning without any measures correspond to ω = 1. Schools closure is 131 achieved by setting ω = 0. The summary of the model parameters is given in Table 1 Model equations

The model was implemented using a system of ordinary differential equations as follows

where S k , E k , R k and H k are the numbers of persons in age group k, k = 1, . . . , n, who are susceptible, exposed, 141 recovered and hospitalized, respectively. The number of infectious persons in age group k and stage p = 1, . . . , m is 142 7 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint denoted I k,p . The force of infection is given by 144 where N k is the number of individuals in age group k, N k = S k + E k + m p=1 I k,p + H k + R k . We took 22 February 145 2020 as starting date (t 0 ) for the pandemic in the Netherlands, which is 5 days prior to the first officially notified 146 case. We assumed that there were no hospitalizations during this 5 day period. As initial condition for the model, 147 we assume that a fraction θ of each age group was infected at time t 0 , equally distributed between the exposed and 148 infectious persons, i.e., E k (t 0 ) = 1 2 θN k , I k,p (t 0 ) = 1 2m θN k and S k (t 0 ) = (1 − θ)N k . where we parameterize the NegBinom(µ, r) distribution with the mean µ and over-dispersion parameter r, such 161 that the variance is equal to µ + µ 2 /r. 162 We calculated the likelihood of the seroprevalence data using the model prediction of the fraction of non-susceptible 

168 Parameters were estimated in a Bayesian framework using methods we developed before [19, 20] . We used age-169 8 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint specific contact rates with ten age groups, defined by the following age intervals [0,5), [5,10), [10, 20) al.

[14] to correct for this discrepancy. The Bayesian prior distributions for the estimated parameters (see Table 1 ) folded-N (1, 0.1) a priori, we expect the reduction in contacts after the first lockdown to account for most of the decrease in the transmission rate t 1 N (23, 7) the mean of t 1 is given by the day of initiation of most drastic social distancing measures (March 15); most measures were taken within two weeks from this date K 1

Exp (1) with K 1 = 1 the uptake of measures takes approximately 6 days θ Uniform(10 −7 , 5 · 10 −4 ) vague prior allowing for approximately 10 0 -10 5 infections at time t 0

Model outcomes 183 We considered control measures aimed at reducing contact rate at schools or in all other locations. Main outcome 184 measures were age-specific seroprevalence and hospital admissions. In addition, we evaluated the impact of a control 185 measure by computing the effective reproduction number (R e ) using the next generation matrix method [18, 22] , 186 and percentage of contacts that need to be reduced to achieve control of the pandemic as quantified by R e = 1.

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Epidemic dynamics 189 The model shows a very good agreement between the estimated age-specific hospitalizations and the data ( Figure   190 2). The number of hospitalizations increases with age, with the highest peaks in hospitalizations observed in persons is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint (95%CrI 50-72%) for persons between 20 and 60 years old ( Figure S3 ). The estimated basic reproduction number CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint pupils to stay at home in case of symptoms or a household member diagnosed with SARS-CoV-2 infection; physical 221 distancing between teachers and pupils (but not between pupils) only applied to secondary schools. We therefore 222 assumed that the effective number of contacts in schools was the same as before the pandemic (ω = 1). For the 223 non-school related contacts we assumed that 1) the number of contacts increased after April 2020 (full lockdown) 224 but was lower than before the pandemic, and that 2) the transmission probability per contact was lower due to 13 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint plemented since the end of August (partial lockdown intended to prevent the second wave) had led to an effective 238 reproduction number of 1.00 (95%CrI 0.94-1.33) (Figure S4 D) , and, as described above, only limited control 239 measures were taken in schools. Now, the impact of interventions targeted at reducing school contacts ( Figure   240 7 B) would reduce the effective reproduction number similarly as reducing non-school contacts in the rest of the 241 population (Figure 7 A) . Specifically, closing schools would reduce the effective reproduction number by 16% (from Figure 7 . Impact of reduction of two types of contacts on the effective reproduction number in November 2020. Percentage reduction in (A) other (non-school related) contacts and (B) school contacts, with the number of the other type of contact kept constant in each of the two panels. The scenario with 0% reduction describes the situation in November 2020. The scenario with 100% reduction represents a scenario with either (A) maximum reduction in other (non-school related) contacts to the level of April 2020 or (B) complete closure of schools. The solid black line describes the median, the shaded region represents the 95% credible intervals obtained from 2000 parameter samples from the posterior distribution. The red line is the starting value of R e (situation November 2020), the green line is the value of R e achieved for 100% reduction in contacts. To control the pandemic, R e < 1 is necessary.

Interventions for different school ages 246 Next we investigated the impact of targeting interventions at different age groups, starting from the situation in 247 November 2020 with the effective reproduction number being 1 (Figure S4 D) . Figure 8 A CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted December 8, 2020. ; https://doi.org/10.1101/2020.12.07.20245506 doi: medRxiv preprint could decrease R e by about 8% (compare Figure 8 C and Figure 7 B where we expect the reduction of 16% after 254 closing schools for all ages). Schools closure for children aged 5 to 10 years would reduce R e by about 5% (Figure 8 CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted December 8, 2020. Figure S1 . Contribution of the contact rate after the first lockdown. We model the transition in the general contact rate, c kl , as follows c kl = [1 − f (t)]b kl + ζ 1 f (t)a kl , where f is the contribution of the contact rate after the first lockdown, b kl and a kl are the contact rates specific to the periods before and after the first lockdown. f is a logistic function with parameters K 1 and t 1 governing the speed and mid-way of lockdown roll-out. The red and gray lines show the median and several individual estimated trajectories, respectively.

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Key questions for