A data-driven metapopulation model for the Belgian COVID-19 epidemic: assessing the impact of lockdown and exit strategies

Abstract

Background: In response to the ongoing COVID-19 pandemic, several countries adopted measures of social distancing to a different degree. For many countries, after successfully curbing the initial wave, lockdown measures were gradually lifted. In Belgium, such relief started on May 4th with phase 1, followed by several subsequent phases over the next few weeks.

Methods: We analysed the expected impact of relaxing stringent lockdown measures taken according to the phased Belgian exit strategy. We developed a stochastic, data-informed, meta-population model that accounts for mixing and mobility of the age-structured population of Belgium. The model is calibrated to daily hospitalization data and is able to reproduce the outbreak at the national level. We consider different scenarios for relieving the lockdown, quantified in terms of relative reductions in pre-pandemic social mixing and mobility. We validate our assumptions by making comparisons with social contact data collected during and after the lockdown.

Results: Our model is able to successfully describe the initial wave of COVID-19 in Belgium and identifies interactions during leisure/other activities as pivotal in the exit strategy. Indeed, we find a smaller impact of school re-openings as compared to restarting leisure activities and re-openings of work places. We also assess the impact of case isolation of new (suspected) infections, and find that it allows re-establishing relatively more social interactions while still ensuring epidemic control. Scenarios predicting a second wave of hospitalizations were not observed, suggesting that the per-contact probability of infection has changed with respect to the pre-lockdown period.

Conclusions: Contacts during leisure activities are found to be most influential, followed by professional contacts and school contacts, respectively, for an impending second wave of COVID-19. Regular re-assessment of social contacts in the population is therefore crucial to adjust to evolving behavioral changes that can affect epidemic diffusion.

Keywords: Behavioral changes; COVID-19; Epidemic modeling; Metapopulation; Mixing patterns; Spatial transmission.

Fig. 1

Schematic representation of the compartmental model: Individuals start as susceptible (S) and can become exposed to the disease (E) when interacting with infected individuals (I_p,I_a,I_ms and I_ss). After a latent period, exposed individuals enter a pre-symptomatic phase (I_p), after which they can either become symptomatic (I_ms and I_ss) or remain without symptoms (I_a). Symptomatic individuals can develop mild symptoms (I_ms) or severe symptoms (I_ss). When symptoms are severe, they are hospitalized (H). The final outcome of infected individuals is either recovery (R) or death (D)

Fig. 2

Model fitting. Data on hospital admissions is shown in comparison with the best-fit model. Black points are used to calibrate the model in the lockdown phase. In both panels median curves are shown along with 50% confidence intervals (CIs; dark shade) and 95% CI (light shade)

Fig. 3

Exit scenarios using different timings and location-specific reductions. a: different implementations of phase 1 (work re-opening). b: different implementations of phase 2 (school re-opening). c: different implementations of phase 3 (leisure re-opening). The top of each panel shows the parameter values used. In all panels median curves are shown along with 50% confidence intervals (dark shade) and 95% CI (light shade). Color-code is consistent across panels, with the same color marking the same scenario in different panels

Fig. 4

Summary of exit scenarios. a: peak value of daily hospital admissions up to the 31st of August. b: number of hospitalizations up to the 31st of August. In both panels the y-axis shows the relative variation with respect to the best-case (least contacts) scenario. A circle denotes the scenario used in the contact isolation analysis (Fig. 6)

Fig. 5

Comparison of model contact matrix and measured ones. a-c: Contact matrices for phase 1 (a), phase 2 (b) and phase 3 (c) in the simulated scenarios. For each matrix element we report the average value and the [min:max] interval over the different implementations of phases 1, phase 2 and phase 3 considered in Fig. 5. d-f: Contact matrices for phase 1 (d), phase 2 (e) and phase 3 (f) measured in a survey representative of the Belgian adult population. For each matrix element we report the average value and the 95% bootstrap confidence interval. Contacts of children participants, not measured in the survey, are marked with “X”. Data from [50], available at [59]

Fig. 6

Effect of case isolation in a specific scenario. a: new hospitalizations per day. b: cumulative number of hospitalizations relative to the no case isolation scenario. All curves are obtained considering 40% of working contacts, 40% of contacts at school and 40% of leisure/other contacts with respect to pre-pandemic period (scenario denoted by a black circle in Fig. 4). In both panels median curves are shown along with 50% confidence intervals (dark shade) and 95% CI (light shade)