Estimating the effects of non-pharmaceutical interventions on the number of new infections with COVID-19 during the first epidemic wave

Abstract

The novel coronavirus (SARS-CoV-2) has rapidly developed into a global epidemic. To control its spread, countries have implemented non-pharmaceutical interventions (NPIs), such as school closures, bans of small gatherings, or even stay-at-home orders. Here we study the effectiveness of seven NPIs in reducing the number of new infections, which was inferred from the reported cases of COVID-19 using a semi-mechanistic Bayesian hierarchical model. Based on data from the first epidemic wave of n = 20 countries (i.e., the United States, Canada, Australia, the EU-15 countries, Norway, and Switzerland), we estimate the relative reduction in the number of new infections attributed to each NPI. Among the NPIs considered, bans of large gatherings were most effective, followed by venue and school closures, whereas stay-at-home orders and work-from-home orders were least effective. With this retrospective cross-country analysis, we provide estimates regarding the effectiveness of different NPIs during the first epidemic wave.

Fig 1. Timing of NPIs by country.

(A) Number of new cases per 100,000 (rolling 7-day mean) when NPIs were first implemented across countries. For countries with regional variation in the implementation of NPIs, the number of new cases was averaged across regions. (B) Timeline of the implementation of NPIs. The horizontal lines show the time period in which NPIs were implemented within each country’s regions. For most countries, there was no regional variation and the NPIs were implemented at one day across the entire country.

Fig 2. Visual summary of the model structure.

(1) the number of new infections is modelled as a function of the number of contagious subjects, the country-specific daily transmission rate, and the reductions from active NPIs; (2) the observed number of new cases is a weighted sum of the number of new infections in the previous days; and (3) the number of contagious subjects is a weighted sum of the number of new infections in the previous days.

Fig 3. Modeling choices for the effects of NPIs.

(A) Time-delayed response function as a first-order spline. (B) Prior for the effects of NPIs θ_m.

Fig 4. Estimated effects of NPIs.

(A) Reduction in new infections (posterior mean as dots with 80% and 95% credible interval as thick and thin lines, respectively). (B) Ranking of the effects of NPIs from highest (1) to lowest (7) (posterior frequency distribution). (C) Frequency of at least m positive effects (posterior frequency distribution). (D) Frequency of at least m effects greater than 10% (posterior frequency distribution).

Fig 5. Summary of the sensitivity analysis.

Sensitivity of the estimated effects of NPIs (posterior mean as dots) to different data preprocessing, varying modeling and prior choices, and data exclusion. Section 6 in S1 Appendix presents all individual sensitivity analyses in detail.

Fig 6. Model fit for four selected countries over time.

Expected number of new infections μ^I and new cases μ^N (posterior mean as colored lines with 95% credible interval as shaded area) and the observed number of new cases by country over time. Red letters and lines indicate the first day an NPI was implemented within a country (S: School closures, B: Border closure, E: Ban of large gatherings, G: Ban of small gatherings, V: Venue closure, H: stay-at-home order, W: Work-from-home order). The non-modeling phase is the time period before 100 cumulative cases were observed, which was used to seed infections in the early outbreak of the epidemic. Plots for all countries are provided in Section 7 in S1 Appendix.