R was 1.04 in Georgia before the lockdown

Good news amidst persistently high incidence of Covid-19: the effective reproduction number R dropped to 1.04 (+-0.02) in Georgia even before new lockdown measures were introduced last week. This bodes well for the effectiveness of the current interventions.

According to these estimates, in the second half of November the average Covid-19 infected person in Georgia transmitted the virus to 1.04 people. Regional estimates vary between 0.90 (+-0.06) in Samegrelo-Zemo Svaneti and 1.22 (+-0.09) in Kakheti. This is significantly down from around 1.3 nationally, and from over 1.5 in many regions, in the first half of October.

The effective reproduction number R is a key metric to monitor the spread of an epidemic. The number of infections is increasing if R is larger than 1 and decreasing if R is smaller than 1.

The estimates at hand are based on state-of-the-art algorithms developed at Imperial College London and ETH Zürich and on regional case numbers published by the National Center for Disease Control (see methodology section at the bottom). Public estimates of R on a regional level have so far been lacking in Georgia.

Estimates of the effective reproduction number R (with 95% confidence band) for Georgia and its regions. A wide confidence band indicates indicate high uncertainity due to low case numbers. Since cases are typically confirmed 1 – 2 weeks after infection, the latest estimates of R reflect the epidemiological situation around 21 November.
Left side: Daily estimates. Values between between 24 September and 17 October (dashed line segment) are unreliable due to a change in testing strategy. Estimates for late September and early October significantly underestimate the true value, while estimates towards the middle of October are slightly above the true value. Right side: Average estimates for time periods between major events and interventions. The estimates for the period between 24 September and 17 October overall slightly underestimate the actual value.
[See methodological section for more details and links to data and source code.]

For Covid-19 in the absence of any interventions or behavioural changes, R was estimated to be around 2.5 – 3 in most countries. This roughly translates to cases doubling every 3 – 4 days. In contrast, the reduction to R=1.04 implies an expected doubling time of 1 – 2 months.

So did the government interventions work?

The right hand side of the figure above shows the average reproduction number between major events or government interventions.

Evidently, the average R dropped considerably in all regions following the night-time curfews introduced on 9 November. This is true even for those regions to which the curfew did not apply.

Moreover, almost all regions experienced a significant decrease of R in the middle of October. This came in the wake of government interventions in Tbilisi, Imereti (16 October) and Mtskheta (20 October), namely restricted opening hours for restaurants, bars and other entertainment facilities. Again, a slowdown of the spreading is observed even in regions to which the measures did not apply.

This could suggest that factors such as the signalling effect of the interventions and more urgent appeals by the authorities had as much of an impact on public behaviour as the actual measures themselves.

The national parliamentary elections on October 31 seem to have been associated with a temporary increase of R in many regions. This is a particularly sensitive point given that the government has repeatedly accused opposition protesters of fueling transmission of the virus. Transmission indeed seems to have risen in Tbilisi in the aftermath of the elections, but even more so in many rural regions during the election weekend.

The figures on the left hand side also show a rise of R at the beginning of October in Tbilisi, Imereti and Kvemo Kartli. This is puzzling given that estimates around that time are expected to have a downward bias due to a change in testing policy on 3 October (see methodology section below). One plausible explanation is that the reopening of primary schools on 1 October in Tbilisi, Kutaisi and Rustavi lead to increased transmission.

What can be expected from the lockdown?

Last week, the government introduced a number of sweeping new measures for the next two months, including the closure of schools, restaurants, bars, gyms and non-essential shops and markets.

Their effect is not yet captured in the estimates presented here, but the figures above bode well for the epidemiological development in the coming weeks: if the lockdown measures have any impact at all, they are set to push R below 1, leading to a substantial reduction in caseload from next week onwards.

Given the economic cost of a prolonged lockdown, the crucial question is not so much if, but how fast the reduction will take place. This depends on the actual amount by which R is reduced. As a rule of thumb, at R=0.9 cases will be cut in half within a month, at R=0.8 within two weeks and at R=0.6 within one week.

The seemingly small difference is in fact a matter of life and death, as a simple projection shows: if R remains very close to 1 during the lockdown, total deaths could rise to 5000 until February – and continue to pile up in spring if the strict measures are not upheld.

Yet in the highly optimistic scenario of constant R=0.6 over the next two months, the country might just about limit its total coronavirus death toll to 2500 until the beginning of March. Crucially, infections by that point would be so low again that the first batch of vaccines announced for spring could be in time to prevent much further carnage, even if the lockdown is not prolonged and R ticks up again. Rarely has it mattered so much how we collectively conduct our lives over the next two months.

An updated version of this article was republished by OC media.

Methodological notes

1. Estimation of R

To my knowledge, the figures presented here are the first public estimates of the effective reproduction number on a regional level for Georgia. The estimates are based on a widely used Bayesian approach developed in 2013 by epidemiologists at Imperial College London. However, their algorithm assumes that we know or are able to infer the exact dates on which patients were infected with the disease. National health authorities typically have this data for a substantial number of patients (or at least the dates of symptom onset), but it is usually not in the public domain. This means that the likely infection dates have to be infered from case confirmation dates. Several methods have been developed to do that. Here, we use a state of the art approach used by the Covid tracking team of ETH Zürich.

Together with my friend Johannes Josi I have implemented this approach as a python package, available here. Please feel free to use it yourself. A tutorial jupyter notebook explains how to apply the package to Covid-19 data.

Without diving too deep into the workings of the algorithm, there are two things to keep in mind when interpreting the output:

a) Slow response to abrupt changes: having to work with the publicly reported cases instead of actual infection dates leaves us with a blurred picture of the real infectious activity. In trying to reconstruct the lost information, we face a trade-off choice: either we infer a highly time-sensitive estimate of R but risk to keep a lot of spurious signals (stemming from such things as weekend underreporting, arbitrary spikes due to a backlog of cases, etc.) or we prioritise an estimate which is highly stable under steady state conditions but has a slow response to fast changes. With my choice of parameters (smoothing_window=21 and r_window_size=3) I opt for stability over detail. As a consequence, if, in reality, R changes abrubtly from one day to the next, estimates of R will need two weeks to pivot from their old level to the new one. Moreover, the estimates start moving towards the new true value before the sudden change has happened in reality. This is a point to keep in mind when thinking about causal links between some event and an associated change in R. The following figure illustrates how the estimates respond to a slow and an abrupt decrease of real R:

The top figure shows how the algorithm responds to a slow and a fast change of the true reproduction number. The bottom figure shows the simulated infection and case numbers created from some initial infections and the given true R.

b) Consistent reporting matters: not all infections are detected and reported. As long as the ratio of reported infections to all infections remains constant over time, the algorithm returns the correct estimate for R. One way to control for underreporting is to monitor the reported deaths. Modelling based on deaths suggests that the fraction of reported cases has remained reasonably stable throughout October and November. However, in early October tests were becoming scarce and on 3 October the testing strategy was changed: henceforth, asymptomatic contacts of confirmed cases have only been tested if and as soon as they had symptoms. Naturally, this must have first lead to a sudden drop in reported cases, followed by a slow rise within 1 – 2 weeks back up to a lower level than before the change. The following figure shows the expected effect of the test strategy change on the estimates of R:

Effect of abrupt change from testing all contacts to testing only symptomatic contatcs (vertical line). For simplicity we assume that daily infections remain at a constant level (blue line in bottom graph). The true reproduction number is thus always 1. The changed testing policy permanently decreases the fraction of infections which are detected (yellow line). The estimate of R reacts to this apparent dip with a downturn followed by a smaller uptick.

c) Inaccurate generation time and reporting delay distributions can introduce a systematic bias: the algorithm assumes known (and unchanged over time) distributions of the generation time (time which passes from infection of individual A to infection of another individual B by A), the incubation time (time which passes from infection to onset of symptoms) and the reporting delay (time which passes from onset of symptoms until the case is reported). In reality, the generation time and reporting delay are known to vary a bit over time and from country to country. Due to the lack of public Georgian data on this, we use empirical distributions as reported in the scientific literature for other countries. If these do not correspond to the actual distributions we may have introduced a small but consistent bias of R towards or away from 1 (in case of inaccurate generation time) or an offset of up to 3 days in time (in case of inaccurate reporting delays). However, these biases do not impact the observed trends.

2. Data source

All estimates are based on daily reported case numbers for Georgia and its regions. Regional numbers have been made public by the NCDC since September 14 (first in daily press briefings and later on their webpage) for most regions and somewhat earlier in Adjara, Imereti and Samegrelo. I have compiled a file with the collected data, available here. Again, please feel free to make use of it.

For the estimation of R I have only included cases up to 1 December, so as not to skew the results by the lockdown measures introduced on 28 November.

3. Change points

The choice of change points in the main figure is somewhat arbitrary and requires justification. Dates of relevant events or changes to government policy in Georgia were:

2 September – superspreading event in Batumi revealed, start of 2nd wave.

10 September – National gatherings ban.

24/25 September – Adjara: restaurants and public transport shut down.

12 October – All kindergardens reopen in Georgia except Adjara and Ozurgeti (Guria)

16 October – Tbilisi and Imereti: restricted opening hours for restaurants/bars etc.

17 October – Tbilisi: kindergardens close again.

19 October – Adjara: partial reopening of public transport.

20 October – Mtskheta: restricted opening hours for restaurants/bars etc.

29 October – Many schools close in preparation for the elections.

31 October – National parliamentary elections. Major street protests in the week after.

4 November – outdoors mask mandate in major cities

9 November – night-time curfews in major cities

21 Novemeber – second round of parliamentary elections (historically low turnout)

24 November – schools in major cities switch back to remote learning

28 November – partial national lockdown (restaurants/bars, retail, public transport, fitness, culture, tourism, extension of night-time curfew, etc.)

Based on this list I chose the following change points (including start and end point) for all regions: 15 August, 10 September, 24 September, 17 October, 29 October, 4 November, 9 November, 21 November. I rejected 1 October as a change point because it falls in the period which is skewed by the changing testing strategy.

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