key: cord-0772538-5wua6mqx
authors: Alleman, Tijs W.; Vergeynst, Jenna; De Visscher, Lander; Rollier, Michiel; Torfs, Elena; Nopens, Ingmar; Baetens, Jan M.
title: Assessing the effects of non-pharmaceutical interventions on SARS-CoV-2 transmission in Belgium by means of an extended SEIQRD model and public mobility data
date: 2021-10-02
journal: Epidemics
DOI: 10.1016/j.epidem.2021.100505
sha: b79acff7078b016b62dbd66280759570a899d17c
doc_id: 772538
cord_uid: 5wua6mqx

We present a compartmental extended SEIQRD metapopulation model for SARS-CoV-2 spread in Belgium. We demonstrate the robustness of the calibration procedure by calibrating the model using incrementally larger datasets and dissect the model results by computing the effective reproduction number at home, in workplaces, in schools, and during leisure activities. We find that schools are an important transmission pathway for SARS-CoV-2, with the potential to increase the effective reproduction number from [Formula: see text] (95 % CI) to [Formula: see text] (95 % CI) under lockdown measures. The model accounts for the main characteristics of SARS-CoV-2 transmission and COVID-19 disease and features a detailed representation of hospitals with parameters derived from a dataset consisting of 22 136 hospitalized patients. Social contact during the pandemic is modeled by scaling pre-pandemic contact matrices with Google Community Mobility data and with effectivity-of-contact parameters inferred from hospitalization data. The calibrated social contact model with its publically available mobility data, although coarse-grained, is a readily available alternative to social-epidemiological contact studies under lockdown measures, which were not available at the start of the pandemic.

After an initial outbreak in early 2020 in Wuhan, China, Severe acute respiratory syndrome coro-1 navirus 2 (SARS-CoV-2) has spread globally [1] . SARS-CoV-2 is capable of sustained human-2 to-human transmission [2] and may cause severe disease and death, especially in older in-3 dividuals. The SARS-CoV-2 pandemic has, in general, shown a remarkably low incidence 4 among children and young adults [3, 4, 5] . Furthermore, presymptomatic transmission is a 5 major contributor to SARS-CoV-2 spread [6, 7] . Both on March 15th, 2020, and on October wanes or if SARS-CoV-2 further mutates, it is expected that SARS-CoV-2 will become en-10 demic [8] . Hence, there is a need for well-informed models and knowledge build-up to 11 assist policymakers in choosing the best non-pharmaceutical and pharmaceutical interven-12 tions during future SARS-CoV-2 outbreaks. 13 14 Currently, four other models exist to inform policymakers in Belgium. The agent-based 15 model (ABM) of Willem et al. [9] , the data-driven model by Barbe et al. [10] and the nation-16 level, age-stratified compartmental models of Abrams et al. [11] and Franco [12] . The models 17 of Abrams et al. [11] and Franco [12] feature similar disease dynamics as our model but rely 18 on different assumptions to model social contact. The different model outputs are currently 19 combined into an ensemble to inform policymakers [13] . In the ensemble, each model fulfills 20 a niche, for instance, the ABM of Willem et al. [9] is good for studying microscopic social be- 21 havior, and was used to inform the optimal household bubble size. The model of Barbé excels 22 at short-term forecasts while our model, together with the compartmental models of Abrams 23 et al. [11] and Franco [12] , are well-fit to study the long-term effects of population-wide in-24 terventions.

In this work, we built a compartmental, age-stratified, nation-level model which accounts 27 for the main characteristics of SARS-CoV-2 disease. The model features a detailed repre-28 sentation of hospitals with residence times and mortalities derived from a large dataset of 29 hospitalized patients in Belgium. We built a social contact model which scales pre-pandemic 30 contact matrices from a study by Willem et al. [14] with the Google Community Mobility 31 data [15] and with effectivity-of-contact parameters derived from hospitalization data us-32 ing an Markov Chain Monte Carlo (MCMC) method [16] . Tardiness in compliance with social 33 restrictions is included using a delayed-ramp model and waning of humoral immunity is 34 included by estimating the rate of seroreversion from two serological datasets. We find that 35 hospitals, we computed age-stratified hospital residence times and mortalities. Using the ob-48 tained parameters, we found the model was able to predict the total number of patients and 49 the number of deceased patients in Belgian hospitals well. We calibrated the model to hos- anti-SARS-CoV-2 antibodies to wane (seroreversion), was estimated as 9.2 months (IQR: 7.2 55 -12.1 months). Using the calibrated model, we computed the relative share of contacts and 56 the effective reproduction numbers and found these to be in line with estimates from other 57 authors at home, at school, at work and during leisure activities to asses their effect on SARS-58 CoV-2 spread during both 2020 COVID-19 waves. We observed a strong correlation between 59 school re-opening and increases in SARS-CoV-2 transmission. More precisely, schools have 60 the potential to increase the effectiveic reproduction number from R e = 0.67 ± 0.04 (95 % CI) 61 to R e = 1.09 ± 0.05 (95 % CI) under lockdown measures.

Throughout the work, Belgium is used as a case but the scope of the work is extendable to 64 other countries. Since February 2021, the effects of new SARS-CoV-2 strains and pharmaceu-

Infected Infectious Hospitalized Figure 1 : Extended SEIQRD dynamics used in this study. Here, S stands for susceptible, E for exposed, I presy for presymptomatic and infectious, I asy for asymptomatic and infectious, Q mild for mildly symptomatic and infectious, Q cohort for cohort, Q ICU,rec for a recovery stay in cohort coming from IC, Q ICU for Intensive Care Unit, D for dead and R for recovered. A subscript i is used to denote the ith age strate of the model, the model has a total of nine age strata. An overview of the model parameters can be found in table 1. This was accomplished by defining a system of K × N ordinary differential equations, one 105 for every of the K = 10 model compartments, each of which is further split into N = 9 106 age-stratified metapopulations. The age groups have different contact rates with other age 107 groups and the disease progresses differently for each age group, making the model behave 108 realistically. Our model consists of 9 age classes, i.e., [0, 10(, [10, 20(, [20, 30(, [30, 40(, [40, 50(, 109 [50, 60(, [60, 70(, [70, 80(, [80, ∞( 

for i = 1, 2, . . . , 9. Here, T stands for total population (Table 1) , S stands for susceptible, E for exposed, I presy for presymptomatic and infectious, I asy for asymptomatic and infectious, Q mild for mildly symptomatic and infectious, H cohort for cohort, H ICU,rec for a recovery stay in cohort coming from Intensive Care, H ICU for Intensive Care Unit, D for dead and R for recovered. A subscript to these variables is used to refer to one of the nine age strata in the model. Using the above notation, all model states are 9-dimensional vectors,

where S i (t) denotes the number of susceptibles in age-class i at time t after the introduction 121 of SARS-CoV-2 in the population. As initial condition, the whole population is assumed 122 susceptible to SARS-CoV-2 and one exposed individual and one pre-symptomatic infectious 123 individual in every age class is assumed, so E i (0) = I i (0) = 1 for all i = 1, 2, ..., 9. 

and the population basic reproduction number is calculated as the weighted average over 160 all age groups using the demographic data in to ω + σ, lasts 5.2 days [6] . CoV-2 have been reported in single cases in the USA [20], Ecuador [21] and Belgium [22] . as the age-stratified recovery time in cohort after a stay in ICU (d ICU,rec ), which were not 243 included by Faes et al. [41] . 3) To obtain age-stratified estimates in nine ten-year age strata 244 as compared to four age strata by Faes et al. [41] . For every patient the following data were Two surges in COVID-19 cases were observed in Belgium, resulting in two lockdowns ( Fig-286 ure 2). The first lockdown was imposed on March 15th, 2020, and lasted until May 4th, 2020, 287 and involved the closure of schools, bars, clubs, restaurants, all non-essential shops, and a 288 closure of the border to non-essential travel (Table 2) . From May 4th, 2020 until July 1st, 2020 Dashed lines indicate the start of the first lockdown on Friday, March 13th, 2020, and the start of the second lockdown on Monday, October 19th, 2020. Increases in the categories residential and parks suggest increased activity around the home environment, while increases in the other categories are more indicative of increases in general mobility [43] . The mobility reduction in workplaces is used to scale the work interaction matrix, the retail & recreation reduction is used to scale the leisure interaction matrix, the groceries & pharamacy reduction is used to scale the other interaction matrix, the transit stations reduction is used to scale the public transport mobility matrix. ther, since the compliance model parameters will be estimated from hospitalization data, the 352 added degrees of freedom aid in obtaining a better model fit to the peak hospitalizations. In 353 our model, we use a delayed ramp to model compliance, i.e.,

where,

where τ is the number of days before measures start having an effect and l is the number of 

where the vector of parameters, θ, that maximizes the log-likelihood function must be found.

In Equation 19 , y denotes the model prediction, x denotes the timeseries of data and N 403 represents the number of datapoints. 

where N * c, home , N * c, schools , N * c, work , N * c, rest denote the number of effective contacts at home,

in schools, at work or for the sum of leisure, public transport and other contacts. The relative 420 share of contacts in location x and for age group i is computed as,

The effective reproduction number for age goup i, in place x and at time t is computed as,

Finally, the population average effective reproduction number in place x, and the population 423 average relative share of contacts in location x, are computed as the weighted average over 424 all age groups using the demographics listed in Table 1 . (Table 5) . 

[ 0, 10[ [10, 20[ [20, 30[ [30, 40[ [40, 50[ [50, 60[ [60, 70[ [70, 80[ [80, [ 

To better compare the effects of non-pharmaceutical interventions between both 2020 COVID-510 19 waves, we computed the relative share of contacts and the effective reproduction number 511 at home, in schools, in workplaces, and for the sum of leisure, public transport, and other 512 contacts (Figure 7) . In this way, we can dissect the force of infection in our model, allowing 513 us to assess the relative impact of contacts made at different locations on SARS-CoV-2 trans-514 mission. In pre-pandemic times, leisure and work contacts account for the bulk of total con- : (First column) Relative share of contacts at home, in the workplace, in schools and for the sum of leisure activities, (Second column) effective reproduction number (R e ) at home, in the workplace, in schools and for the sum of leisure activities, other activities and public transport. The right axis denotes the predicted number of daily Belgian hospitalizations. The first row depicts the first COVID-19 wave in Belgium, from March 15th, 2020 until July 14th, 2020, while the second row depicts the second COVID-19 wave in Belgium, from September 1st, 2020 until February 1st, 2020. Mean and 95 % confidence interval of 1000 model realisations. The background is shaded grey before lockdown measures were taken. During both lockdowns, home interactions have the largest share of effective contacts. During lockdown release, the relative importance of work and leisure contacts start increasing. Schools opening and closing has a large impact on the effective reproduction number, and can end a decreasing trend in hospitalizations. 18). The seroreversion rate 594 was estimated using two serological datasets. The data by Herzog et al. [39] consists of 595 residual blood samples sent to laboratories, while the dataset of Sciensano consists of blood 596 samples from Red Cross blood donors. The dataset of Herzog et al. [39] is likely biased to-597 wards sick individuals, while the dataset of Sciensano is biased towards healthy individuals.

In the calibration procedure, both datasets were given equal weights to incorporate a truth 599 in the middle heuristic. We estimated the average time to seroreversion as 9.2 months (IQR: Coletti et al. [17] shows that younger individuals tend to increase their 650 contacts sooner than older individuals after the release of lockdown measures. These dif-651 ferential effects are still captured in our social contact model, albeit less accurate than the 652 survey-based contact model, by the multiplication of the GCMRs with the pre-pandemic 653 number of contacts. For example, the mobility reduction in workplaces is only applied to 654 the matrix of work contacts, which only contains contacts for individuals between 20 and 655 60 years old. Further, because the GCMRs are collated smartphone data, one could expect 656 the elderly population to be underrepresented due to lower smartphone usage. However, 657 it is unlikely that this would drastically alter our study's results because older individuals 658 have fewer contacts than younger individuals and thus contribute less to overall SARS-CoV-659 2 spread. 662 Finally, we would like to discuss the importance of schools in the SARS-CoV-2 pandemic. As 663 previously mentioned in section 3.3, there seems to be a strong correlation between school 664 re-opening, the rise of laboratory-confirmed cases amongst youths, the rise of the number in this study. However, this will not alter the large impact schools seem to have on SARS-672 CoV-2 spread in our model. If the susceptibility and infectiousness in children is lowered, 673 this will most likely be countered during the parameter inference, where we expect higher 674 values for the effectivity of contacts of children in schools (Ω schools ) to be inferred. Although 675 the present evidence is circumstantial, and correlation does not imply causation, schools 676 seem to play a critical role in SARS-CoV-2 spread. Thus, school closure seems an effective 677 way of countering an epidemic SARS-CoV-2 trend. The combination of the deterministic epidemiological model, which incorporates a-priori 691 knowledge on disease dynamics, and the social contact model whose infectivity parameters 692 were inferred allow us to make the most out of the available pre-pandemic data and public 693 mobility data. Our method is computationally cheap and does not require ad-hoc tweaking 694 to obtain a good fit to the observed data. A disadvantage is that the effectivity parameter dis-695 tributions only converge to their correct posterior distributions a posteriori policy changes.

predictions of the future number of hospitalizations, highlighting the robustness of the cali-698 bration method.

As soon as schools were re-opened on November 16th, 2020, the number of confirmed cases 701 amongst youths starts increasing. A significant lead relationship between the number of 702 cases amongst youths and the working population, and youths and the senior population 703 was found. Our model incorporates this correlation as high effectivities of school contacts.

When schools were re-opened under lockdown policies, the model indicates the effective 705 reproduction number increased from R e = 0.66 ± 0.04 to R e = 1.09 ± 0.05. Thus, school 706 closure is an effective measure to counter an epidemic SARS-CoV-2 trend. • The calibration procedure should be repeated using pandemic social contact matrices, 709 which are currently being gathered for Belgium by Coletti et al. [17] . Further, the ef-710 fects of integrating the contacts with their duration should be explored. A comparison 711 between the different results can then be made.

• The effective reproduction number in the different places should be compared to data 713 on SARS-CoV-2 clusters to further validate the model.

• It is expected that lockdown measures in Belgium will be lifted soon. The impact of re-715 leasing measures on the daily hospitalizations should be studied to find a link between 716 the effectivity parameters and the mobility reductions.

• If schools are a major contributor to SARS-CoV-2 spread, administering a vaccine with 718 high transmission-blocking potential to youths is expected to have a similar effect as 719 schools closure. Due to their localized nature, vaccination for SARS-CoV-2 in schools 720 is logistically easier than vaccinating the general population. 

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