key: cord-0984188-uvdaxa7x
authors: Anderson, Sean C.; Mulberry, Nicola; Edwards, Andrew M.; Stockdale, Jessica E.; Iyaniwura, Sarafa A.; Falcao, Rebeca C.; Otterstatter, Michael C.; Janjua, Naveed Z.; Coombs, Daniel; Colijn, Caroline
title: How much leeway is there to relax COVID-19 control measures?
date: 2021-03-18
journal: Epidemics
DOI: 10.1016/j.epidem.2021.100453
sha: 077866d4f7f257d159fa7bae441fc11adbc4f8fc
doc_id: 984188
cord_uid: uvdaxa7x

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 [Formula: see text] 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 provide 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.

Introduction e novel severe acute respiratory syndrome-coronavirus (SARS-CoV-virus) , which emerged at the end of , has caused a global pandemic with over million con rmed cases of coronavirus disease (COVID-) and , con rmed deaths worldwide as of September ,

. Wide-ranging non-pharmaceutical interventions (NPIs) such as hand hygiene, face masks, physical (social) distancing, banning mass gatherings, and strict lockdowns have been among the primary tools for reducing COVID-'s spread throughout . -As a result, incidence in many jurisdictions outside China followed a similar pa ern. A er an initial phase of occasional detection (typically during late January to February and commonly due to imported cases), case counts grew rapidly (typically during early March). At this point, NPIs were put in place, in the form of "lockdowns" or other requirements for social and physical distancing. Case counts generally continued to rise for several weeks until the impact of NPIs became observable as a a ening and then decline of the epidemic curve. e economic, social, and health costs of NPIs have been signi cant.

Following declines in incidence, many jurisdictions partially li ed restrictions and reopened their economies, and allowed travel across regional and international boundaries. -Large studies undertaken in high-prevalence se ings do not indicate that herd immunity has been reached, , and consistent with that observation, there have been large resurgences in COVID-cases in some jurisdictions, particularly in the United States. e degree of exibility, or "leeway", that exists to increase activity without causing a major resurgence or "second wave" of cases is largely unknown. e exibility that exists in a given location is dependent on the local circumstances governing transmission, as well as the restrictions that are currently in place. , It is essential to estimate the risk associated with increased social and economic activity, and to understand this risk within and between particular jurisdictions, before making decisions around reopening.

We propose that discussions of COVID-risk in the context of reopening local economic activity, and of reopening borders and trade, should consider three aspects of transmission dynamics: ( ) the probability that infections are rising at the current time in a jurisdiction, even if reported cases are declining; ( ) the probability that a given increase in social and economic activity in the general population will lead to a substantial growth in cases over the coming weeks, and ( )-with regards to travel and border reopening-the number of introduced cases and their likely impact in the destination.

J o u r n a l P r e -p r o o f Using a mathematical model t to local case data for a selection of jurisdictions with di ering epidemics, we estimated the leeway for reopening without causing increasing COVIDcases, and the probabilities that reopening would lead to cases increasing above thresholds after a xed time. We used case data prior to June , and compared the results to subsequent epidemic dynamics. e model includes a portion of the population engaging in distancing and related measures: these individuals are at reduced risk of encountering infectious individuals and are less likely to be encountered themselves-for example because they are able to work from home, consistently wear masks, or avoid social situations (see Methods).

For each of jurisdictions worldwide, selected for their diversity of epidemic trajectories and NPIs, we rst estimated the impact of widespread NPIs in the period between March and late April, , and then calculated how close the estimated contact rate was to the threshold for epidemic growth. ese jurisdictions were chosen to be illustrative rather than a global comparison. We included some European, Asian, and North American jurisdictions with varying epidemic trajectories and included some nations and some states or provinces that are likely to be sources of importations for each other. We estimated this both in the period immediately following NPI measures (late March to the end of April) and a er May , as some jurisdictions began to reopen in May. We refer to these time frames as "post-NPI" and simply "May " (though data go to June ). We use the idea of leeway to describe the room between their state a er May and the threshold beyond which cases would begin to grow.

We obtained reported case data from publicly available sources (Table S ) . In some cases, we performed additional data processing to account for data anomalies prior to model ing (Supplement). We used Google mobility data, along with segmented regression (Fig. S ; Supplement) , to inform Bayesian priors for the start and end dates of physical distancing measures. Figure : S ematic of the epidemiological model. Compartments: susceptible to the virus ( ); exposed ( 1 ); exposed, pre-symptomatic, and infectious ( 2 ); symptomatic and infectious ( ); quarantined ( ); and recovered or deceased ( ). Recovered individuals are assumed to be immune. e model includes analogous variables for individuals practicing physical distancing: d , 1d , 2d , d , d , and d . Solid arrows represent ow 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 can begin distancing and move to the corresponding compartment d at rate d . e reverse transition occurs at rate . e model quickly se les on a fraction = /( + ) participating in distancing, and dynamics depend on this fraction, rather than on the rates and . Reproduced from Ref. for clarity. partment and a reduced duration of infection (compared to the clinical course of disease). We modeled a xed portion of the population that is able to participate in physical distancing; each of the SEIR compartments has an analogous compartment in the distancing group ( Fig. ) . We extended the model here by estimating additional parameters: the timing of the physical distancing ramp, the scale of the initial cases, the fraction of the population engaging in physical distancing, and multiple contact rates through time for those practicing distancing. e model describes the time dynamics of susceptible ( ), exposed ( 1 ) exposed and infectious ( 2 ), symptomatic and infectious ( ), quarantined ( ) and recovered or deceased ( ) individuals ( Fig. ) . It assumes that recovered individuals are immune to the virus. e model has analogous states for individuals practicing physical distancing, given by d , 1d , 2d , d , e system of di erential equations for the non-physical-distancing population is given by:

where is the transmission rate, is the physical distancing parameter, is the average infectious period, d and are the rates individuals move to and from the physical distancing compartments, 1 is the rate of moving from 1 to 2 , 2 is the rate of moving from 2 to , and is the quarantine rate for movement from compartment to . In the model without interventions (neither distancing nor quarantine), the basic reproductive number 0b is ( + 1/ 2 ), namely the transmission rate times the mean duration of the infectious state period. We explicitly estimated 0b not , and so is given by = 2 0b /( 2 + 1). e analogous system of equations for the physical-distancing population is given by:

( )

In this model, the probability of quarantine is /(1/ + ) = 0.2, as the times from onset of symptoms to quarantine and from onset of symptoms to removal are independent exponential random variables.

arantined individuals are unable to infect others in our model, so this would imply isolation outside of the household or a similar situation. e incubation period in our model is the sum of the duration of states 1 and 2 , which is days on average, consistent with published estimates. , e duration of the infectious state is on average days, given and , plus an average of day pre-symptomatic infectiousness. is results in serial intervals on average of -days ( days from incubation period in the infectee, plus between -and days from symptom onset of infector to exposure of infectee, exponentially distributed), consistent with published estimates. While many individuals with symptoms should isolate immediately upon noticing COVID-symptoms, others may not show symptoms at all; a -day duration is an average over this variability. e force of infection for this population is a fraction of that of the non-distancing population Eq. ( ). In addition, note that the factor appears twice in the force of infection. is is due to the fact that physical distancing helps in reducing the rate that "distancers" move about and contact others, and the rate at which they are contacted by anyone (distancing or otherwise) who is experiencing population contact. is factor changes with time to model the introduction and strength of NPI measures that reduce contact rates:

compensate for variable testing through time where possible (Supplement) and for the delay between symptom onset and case reporting (next section).

We determined the threshold that would result in epidemic growth ( ) by projecting with the model under a sequence of values and determining the minimum value that would result in an increase in infectious individuals over time ( + ). We then calculated "threshold ratios", or leeway, as 1 / and 2 / .

We let denote the number of recorded cases on day . e number of people who become symptomatic on a given day is the number moving from the exposed pre-symptomatic ( 2 and 2d ) to the symptomatic ( and d ) compartments, namely ∫ −1 2 [ 2 ( ) + 2d ( )] d . e expected number of reported cases on day is a weighted sum of those who become symptomatic in previous days, where the weights are determined by the the delay between symptom onset and reporting:

where represents the sampling fraction on day and we use a Weibull distribution with shape MLE and scale MLE for (·). If = 1, then all estimated infectious people are tested and then become reported cases; < 1 represents a reduction in expected cases on day due to not everyone being tested. See Ref. for further details on ing (·) from data. We used MLE and MLE as estimated for British Columbia in Ref. for the other regions (due to a lack of the necessary data), except for New Zealand for which A. Lustig and M. Plank (pers. comm.) ed non-public data using our code.

We t our SEIR models with Stan . . , and R . . using our R package 'covidseir'. We sampled from six chains with iterations per chain and discarded the rst half of each chain as warm-up. We assessed chain convergence with trace plots and via ensuringˆ ≤ 1.03 (the potential scale reduction factor) and ESS > 200 (the e ective sample size) ( Table S ) . Code to reproduce our analysis is available at https://github.com/caro ineco ijn/ eeway-reopen-covid19 and insert-Zenodo-archive-ink-on-pub ication.

We found that a er initial NPI measures took e ect, some jurisdictions had substantial leeway to re-open (Japan, New Zealand, New York, Germany, Belgium, and British Columbia), with an above-. probability that contact rates were below % of the threshold for epidemic growth (Fig. A) . Japan and New Zealand had the most leeway, with contact rates well below half the threshold. In contrast, some jurisdictions had li le leeway (the United Kingdom [UK], Washington, and Ontario) and some had none, as cases were still rising ( ebec, Sweden, and California). Estimates for the period a er May found that some jurisdictions had li le or no leeway for further re-opening (California, Sweden, Washington, Ontario) as they were at or above the critical threshold. Some had used part of their leeway already (Japan, Germany, New York, and British Columbia; Fig. A ). Several had more leeway a er May than they did immediately a er NPI measures took e ect (the UK, and ebec, with ebec well below the threshold and the UK with > . probability of being < % of the threshold). New Zealand had so few cases that estimation with this modelling framework le considerable uncertainty. We forecasted the impact of relaxing distancing measures by increasing contact rates among those engaged in distancing, starting from a baseline of the lower of the post-NPI and May estimates (Fig. B-M ). e UK, Belgium, and ebec moved to stricter control a er May . All had some leeway by early June, though we found that increasing contact beyond % above the recent estimate would likely lead to a growing epidemic in the UK and ebec. Belgium had substantial leeway to re-open. e remaining jurisdictions had used some of their leeway already by early June, . ose with li le to no leeway to begin with now showed rapid forecasted increases if contact were to increase (California, Sweden, Washington, and Ontario). British Columbia had some leeway to re-open and did so; a doubling of contact compared to the post-measures baseline predicted rises in case numbers. Germany, New York, New Zealand, and Japan showed low risks of rising cases with moderate increases in contact rates. Comparing our forecasted cases from early June to late August with realized We estimated the probability of exceeding the peak number of cases in March and April, and the probability of reaching one incident reported case per , individuals under different increases in contact rates (again from a baseline of the time period in which control was stricter) (Fig. ) . Given similar increases in contact rate, Ontario, Washington, Sweden, and California were most likely to exceed both one incident case per , and their historical peaks in June and July. e UK had a small risk of exceeding its previous peak (probability of . with a doubling of contact rates from the post-measures period). New York, the UK, and ebec had some risk of exceeding one case per , given these increases; New York's previous peak was high and the risk of exceeding it was correspondingly low.

ere has been pressure to reopen borders to business and leisure travelers due to the social and economic costs of travel restrictions. We modelled the impact of introducing successful imported cases (cases that result in a secondary infection) at a constant rate to estimate the Figure : Cases resulting from one successful import per week over 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 % and % 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.

J o u r n a l P r e -p r o o f impact on total cases in each jurisdiction, taking uncertainty in the contact ratios (and other posterior estimated quantities; see Supplement) into account (Fig. ) . Our results illustrate the expected extra cases resulting from one successful imported case per week over six weeks. Assuming independence of imported cases, these results can be scaled to realistic rates of importation (e.g., for successfully imported cases, multiply expected extra cases by ). In Japan, where the dynamics were well below the threshold in all posterior samples, each importation results in few additional cases. Meanwhile, in California or Sweden, because there was a high posterior probability that transmission was above the threshold, introduced cases were more likely to cause extended chains of transmission and contribute large case volumes.

e result is that up to approximately new cases may result (over six weeks) from a weekly introduction of a single case. Fig. is generated under the assumption that successfully introduced cases join the general population, have access to its testing and control procedures, and engage in its broader distancing and NPI behaviors.

Our forecasted cases from early June to late August with contact rate increases from one-to two-fold were consistent with realized cases in most jurisdictions. California proceeded with reopening in June, under a mandate to wear masks indoors and outdoors if distancing was not possible (June ), but with virus counts and hospitalizations rising, closed bars and other venues at the end of June. Cases peaked in late July at over , daily cases following a new statewide closure of all indoor businesses on July . Cases in New York continued to decline. ebec saw a rise through July and reopened with an extensive array of control measures in place including mask mandates and measures for bars, restaurants and other indoor social venues. British Columbia proceeded with reopening through the summer and saw increases in community transmission, initially among younger age groups. Washington saw similar rises in young adults who were gathering in large numbers. Reopening was paused in response and indoor service at venues selling alcohol was stopped; a decline in cases began in late July. Germany's case counts remained low until late July when a rise began, a ributed to summer travel and increased mobility and contact.

In contrast, some jurisdictions experienced trajectories outside or towards the extremes of our projections. Sweden had restrictions on gatherings, half the workforce working at home, widespread voluntary distancing, and high schools were operating with distance J o u r n a l P r e -p r o o f learning. , In June and July, municipalities took over ensuring that restaurants and bars were following guidelines; elementary schools closed for the summer and testing and contact tracing were enhanced (June ). Sweden's case trajectory was lower than it would have been had contact rates increased according to our forecast, as was the trajectory in Ontario. Whereas in Japan, following reopening of schools, theatres, cinemas, gyms and other indoor events with fewer than people (June ), people (June ), and people (July ), and increases in testing by about %, there was a considerable resurgence of cases likely driven in part by increases in local tourism (subsidised as of July ). Belgium resumed schools on May , reopened bars and restaurants on June th and EU borders on June (while also beginning to test close contacts of cases rather than focusing on symptomatic individuals only). Pools, wellness centers, theatres, casinos, conferences and other indoor venues with limits of people ( with approval) were opened July . ere was then a quick response to rising cases, with social contact limited to per week (July ) and then only per family (July ), mandatory masks and other measures, a er which case numbers returned to a decline by late August. e estimated dates that NPI measures took e ect ( 1 and 2 ) matched dates of policy changes such as mass gatherings or stopping essential services in many but not all jurisdictions. e di erence in some cases is understandable as these measures do not capture infectious contact in the population. e most pronounced di erences between inferred dates when distancing ramped up and timings of these particular measures were in ebec and Ontario, where the model estimated that distancing continued to ramp up well a er the time that essential services were closed, and in Japan, where the model estimated distancing ramping up well a er when mass gatherings were stopped. In ebec and Ontario, transmission within the health care system was captured in our model to some extent with health care in the non-distancing population, but this was probably not greatly impacted by changes in mass gatherings and non-healthcare activities. In Japan, returning travellers in late March contributed to the rise in cases, which was then suppressed by further distancing measures.

To interpret these results with reference to borders and travel requires consideration of the individual jurisdictions involved. Consider a border opening from jurisdiction A to jurisdiction B. If both jurisdictions are well below their thresholds, then the probability of a large volume of new cases resulting from introductions is low, primarily because general transmission will be prevented in jurisdiction B, but also because prevalence is likely to be low in A, though this depends on the epidemic, testing, reporting, and population dynamics in A. Conversely, if A is near its own threshold, then there may be as-yet-unobserved exponential growth of cases in A, a ecting the rate of introduction to B. If the destination is near its threshold, then introduced cases could result in exponential growth in B. Furthermore, travel itself may result in additional transmissions. ese e ects could be ampli ed if travelers join a congregate se ing or are less socially distanced than the general population due to tourism or work activities, or if they have reduced access to local health care and control measures such as contact tracing. Indeed, Ontario, California, Washington and other jurisdictions all saw COVID-outbreaks among farm workers,and more than workers tested positive in Ontario in the weeks up to mid-July, . e COVID-pandemic has seen an unprecedented number of travel restrictions and border measures, in spite of WHO recommendations against unnecessary closures, weak evidence that these are e ective in preventing pandemic in uenza (though they do reduce spread and buy time ), and concerns about their impact on movement of medical supplies and personnel.

ere has been a notion of "travel bubbles" in which countries or jurisdictions experiencing comparable levels of risk open borders to travel and commerce. As jurisdictions with low case numbers reopen their economies (likely approaching the epidemic threshold as measures are relaxed), they will be at renewed risk of introductions. We suggest that the highest-risk borders arise when a source jurisdiction has prevalent cases and the destination jurisdiction is near or above its threshold, or is reopening to the extent that cases could now spread widely despite earlier successes. Due to variations in testing, we do not know the relative prevalence, but we would predict, among the locations in our study, that introductions into California, Sweden, Ontario, and Washington carry the highest risk, followed by the UK. Interactions among these jurisdictions would carry the highest risk, despite that by some indicators the overall COVID-control in several of these is similar. Interactions among the UK, ebec, BC, NY, Germany, and Belgium are lower risk but the probability of causing dozens of new cases per introduced case per week remains considerable. Furthermore, jurisdictions with small historical peaks (e.g., British Columbia, New Zealand) could easily be put in a position of exceeding their historical peak as a result of introduced cases from a region with higher prevalence. e model and underlying data have limitations. e data are provided by jurisdictions and depend on testing protocols and capacity, delays to reporting, di erent base populations being tested, and other variations. Indeed, this motivates using inferred summaries like the leeway, in lieu of direct comparisons of case counts. Our approach accounts as much as possible for J o u r n a l P r e -p r o o f di erences in testing through time, for the local dynamics of distancing behavior, and di erent starting intensity and timing of di erent epidemics. However, our model estimates are oriented towards widespread NPI and distancing measures, and implicitly a ribute changes in case dynamics to contact rates. Transmission dynamics involve a complex interplay of outbreak control, management of COVID-in health care se ings, reduction in community transmission, testing and reporting, contact tracing and other public health measures. Our notion of contact rates combines both rate of interaction and probability of infection during interaction; thus, increased rates of interaction during reopening may, to a certain degree, be possible without increased transmission if key public health measures are in place and highly functional. Our model also assumes a simple population structure-data for more complex population structures being largely lacking. e numbers of reported cases per prevalent case will change as testing is widened, and this is not modelled in our forecasts. Finally, facing rising case numbers, policy-makers are likely to act as they did in California, Washington, Belgium and other areas. Model forecasts based on constant estimated parameters do not take policy and societal reactions into account, though control theory models can do so. Our projections are not intended to be predictions, as any prediction would require some knowledge of the public health and broader responses to the state of the pandemic. e e ective reproduction number (the average number of secondary infections per infection) is the leading concept playing the role of leeway in pandemic reporting and discourse. When < 1, infections decline on average, and they grow when > 1. is simple and interpretable and one might ask whether leeway has any advantage given the speed and simplicity of estimating , for example with packages such as EpiEstim. Even more simply, one could t a regression of log(case counts) ∼ to estimate a rate of growth, . How much below zero the slope is would be akin to the leeway.

is would require even fewer assumptions than ; estimates rely on a generation interval distribution, and generation intervals are hard to measure and are known to change over outbreaks and epidemics. Our model is more complex still, estimating not just a rate or a number but a set of parameters a ached to a mechanism-contact rate among those distancing. Our approach can therefore, in principle, explore what happens if increased screening or testing reduce the duration of infectiousness and continued social distancing measures (for which one now has an estimate of ) are in place. Conversely, the model can project the leeway a orded by expanded testing, improved support for distancing, or other measures. In other words, estimation in a mechanistic model carries advantages in interpretability and use. An estimate, or a growth rate estimate, can-J o u r n a l P r e -p r o o f not be used in the same way. is increased interpretability has proven useful to government agencies in practice: the British Columbia provincial government and the Canadian federal government have both been using estimates of and leeway from these models for decision making since April and September , respectively. Amidst di ering epidemics and control measures, each jurisdiction has a leeway-the room between the current state and the threshold-and this is comparable from place to place. e leeway, together with model ts that are informed by data and which describe the uncertainty in how much leeway there is, can provide a quantitative basis for decisions about reopening. We are at a unique time in this pandemic, with a so-called " rst wave" receding not due to immunity, but due to widespread behavioural change. Given that reopening is occurring, this le populations vulnerable to resurgence of cases, driven both by local transmission and sparked by introductions. To mitigate risks associated with imported cases and reopening borders, it is important to account for the risk of growth in the general population together with the likelihood that imported cases will arrive in high-risk se ings. We recommend that policy-makers carefully consider (i) whether imported cases and seeded outbreaks are likely to be identi ed and managed to the same degree as those in the local population; (ii) whether travellers will engage in high-risk or high-contact activities, especially within marginalized populations; and (iii) whether local trace and test strategies have the capacity to manage imported cases and nascent outbreaks.

is work was supported by funding from the Michael Smith Foundation for Health Research and from Genome BC (project code COV-). C.C. and J.S. are funded by the Federal Government of Canada's Canada Research Chair program. We thank two anonymous reviewers for comments that greatly improved this manuscript. .

Non-Pharmaceutical Interventions (NPIs) to Reduce COVID

Ngatu Nlandu Roger, Hirao Tomohiro. Trends in COVID-Outbreak in Tokyo and Osaka from

E ect of Internationally Imported Cases on Internal Spread of COVID-: A Mathematical Modelling Study e

Advocates demand Ontario shut down farms as COVIDcases soar among workers

Coronavirus Hits Nation's Key Apple