How much leeway is there to relax COVID-19 control measures?

Abstract

Following successful non-pharmaceutical interventions (NPI) aiming to control COVID-19, many jurisdictions reopened their economies and borders. As little immunity had developed in most populations, re-establishing higher contact carried substantial risks, and therefore many locations began to see resurgence in COVID-19 cases. We present a Bayesian method to estimate the leeway to reopen, or alternatively the strength of change required to re-establish COVID-19 control, in a range of jurisdictions experiencing different COVID-19 epidemics. We estimated the timing and strength of initial control measures such as widespread distancing and compared the leeway jurisdictions had to reopen immediately after NPI measures to later estimates of leeway. Finally, we quantified risks associated with reopening and the likely burden of new cases due to introductions from other jurisdictions. We found widely varying leeway to reopen. After initial NPI measures took effect, some jurisdictions had substantial leeway (e.g., Japan, New Zealand, Germany) with > 0.99 probability that contact rates were below 80% of the threshold for epidemic growth. Others had little leeway (e.g., the United Kingdom, Washington State) and some had none (e.g., Sweden, California). For most such regions, increases in contact rate of 1.5-2 fold would have had high (> 0.7) probability of exceeding past peak sizes. Most jurisdictions experienced June-August trajectories consistent with our projections of contact rate increases of 1-2-fold. Under such relaxation scenarios for some regions, we projected up to ∼100 additional cases if just one case were imported per week over six weeks, even between jurisdictions with comparable COVID-19 risk. We provide an R package covidseir to enable jurisdictions to estimate leeway and forecast cases under different future contact patterns. Estimates of leeway can establish a quantitative basis for decisions about reopening. We recommend a cautious approach to reopening economies and borders, coupled with strong monitoring for changes in transmission.

Keywords: Bayesian; COVID-19; Non-pharmaceutical interventions; SARS-CoV-2; SEIR.

Fig. 1

Schematic of the epidemiological model. Compartments: susceptible to the virus ($S$); exposed ($E_1$); exposed, pre-symptomatic, and infectious ($E_2$); symptomatic and infectious ($I$); quarantined ($Q$); and recovered or deceased ($R$). Recovered individuals are assumed to be immune. The model includes analogous variables for individuals practicing physical distancing: $S_{\mathrm{d}}$, $E_{1\mathrm{d}}$, $E_{2\mathrm{d}}$, $I_{\mathrm{d}}$, $Q_{\mathrm{d}}$, and $R_{\mathrm{d}}$. Solid arrows represent flow of individuals between compartments at rates indicated by the mathematical terms. Dashed lines show which compartments contribute to new infections. An individual in some compartment $X$ can begin distancing and move to the corresponding compartment $X_{\mathrm{d}}$ at rate $u_{\mathrm{d}}$. The reverse transition occurs at rate $u_r$. The model quickly settles on a fraction $e=u_d∕(u_d+u_r)$ participating in distancing, and dynamics depend on this fraction, rather than on the rates $u_d$ and $u_r$.

Fig. 2

Projected cases given scenarios of relaxed control measures strongly depend on the leeway between the estimated contact rate and the threshold for increase. A: Posterior densities of the ratio between the contact rate and the threshold (the value above which exponential increases are expected). Darker violins represent the post-measures period and paler dotted violins represent the post-May 1 estimates. Jurisdictions with contacts well below the threshold have more leeway to relax control measures. Colors represent countries (to group the three Canadian provinces and three US states together). B–M: Model fits and projections at 6 multiplicative contact rate increases, from a baseline from the lower of the estimates from the two time periods. Solid lines represent posterior medians and ribbons represent 90% credible intervals. Thin lines represent reported case data. Vertical gray bands indicate 90% credible intervals for the start and end times of initial control measures ramp. Dashed vertical lines indicate the start of the “recent” period (May 1). The choice to project from a baseline of the lower of the post-measures and recent estimates means that projections are based on measures at the stricter time period in all jurisdictions. Gray shaded areas indicate time periods for which data were not used for estimation. Regions are arranged by decreasing mean threshold ratio in the immediate post-measures period.

Fig. 3

Probabilities that cases would exceed reference thresholds over the 6 weeks following June 7, 2020 depend on contact rate increases and jurisdiction. Projections are from a baseline of the lower of the post-NPI and May 2020 estimates. A, B: Probability of exceeding the historical “first wave” maximum. C, D: Probability of reported cases per day exceeding 1/20,000 of the population ($N$). ON: Ontario, WA: Washington, CA: California, QC: Quebec, BC: British Columbia, NY: New York, SE: Sweden, UK: United Kingdom, BE: Belgium, DE: Germany, NZ: New Zealand, JP: Japan.

Fig. 4

Cases resulting from one successful import per week over 6 weeks range from fewer than ten to hundreds and depend on contact in the destination population. Dots represent medians and thick and thin line segments represent 50% and 90% credible intervals; the $x$-axis is log distributed. Contact rate increases are based on the lower of the post-measures and recent contact ratio estimates. Regions are ordered by the average extra cases across contact rate increases. Extra cases are compared to a projection that does not include weekly successful imports; travelers themselves have not been removed from the totals.