The Exponential Decay Model
Here are three simple, baseline scenarios for how a theoretical version of Georgia’s pandemic might go.
This very simple model works by taking the weekly case total for August 27th and multiplying it by a constant ratio, once every week. The orange line is what you get when that ratio is 0.9 - when cases decline by 10% each week. The yellow line shows a ratio of 0.8 (20% decline each week), and the blue line shows a ratio of 0.7 (30% decline each week).
This ratio is not exactly the “R” value, or reproductive rate, of the virus. The R number is applied every time the virus has time to jump from one person to the next - thought to be about five days for the original strain and about three days for Delta. Nevertheless, I find this seven-day ratio useful for making projections and intuitive for thinking about the growth or decay rate of the virus. Generally, when I refer to the growth rate in reported cases, it is this 7-day ratio that I am thinking about. This "growth rate” is usually quite close to other estimates of R, such as the ones made using this much more complicated python project. For the purposes of convenience I often refer to this weekly growth rate as r.
As you can see, the growth rate (or decay rate, as we call it when it’s below 1) that looks like it follows our current trend is 0.9 (as of today, the actual growth rate for the last 7 days is 0.856). One could look at that and be pessimistic, because the orange curve doesn’t drop to pre-Delta levels at any point in the next two months. However, r has been trending downwards since restrictions kicked in about two weeks ago, so it’s entirely plausible that it might continue dropping and settle in at 0.8 or perhaps even 0.7. It reached down all the way to 0.6 on the downward slope of the second wave - however, we had both strict lockdowns and big swings in testing numbers due to the winter holiday, so I doubt we’ll see comparable numbers this time around.
At our current testing rate of about 300,000 tests per week, we’d need to have fewer than 12,000 new cases per week in order to hit a positive test rate below 4%, which is the benchmark Georgia’s public health officials have set for safely reopening schools. However, typically test counts decline as cases decline (due presumably to less demand for tests) and historically a positive test rate of 4% has corresponded to about 7,000 new cases per week.
According to these projections, weekly growth rate of 0.9 would get us below 12,000 cases right around the end of October, and below 7,000 cases around the beginning of December (not shown on the graph). At 0.8, which I think is the most likely of these projections, we’d drop below 12,000 by late September and 7,000 by mid-October. At 0.7 - an optimistic but plausible number, if restrictions are maintained and enforced - we could go below 12,000 by mid-September and below 7,000 by late September.
Note that under no scenario here do we get below 7,000 cases by the time school would normally start, which means that if the Ministry of Education follows the NCDC recommendations, we’re going to start school remotely again this year. Amiran Gamkrelidze, head of the NCDC, agrees.
Variables
The major variables that I’m aware of which might impact our forecast are:
Vaccinations
NPIs (e.g. transit closures, curfews, school postponement)
High-transmission events (holiday gatherings, elections)
In order to consider how these factors relate to the curves in my forecast model, I will be discussing them in terms of their impact on the weekly growth rate (r). Briefly: I believe vaccinations will have little if any noticeable effect on r during the time frame in question, I believe NPIs will continue to be the major determining factor for r, and I believe high-transmission events may sometimes have small, temporary impacts on r but will not be a major factor impacting how the end of this wave plays out.
Vaccinations
Vaccinations are absolutely great for individuals, and if we vaccinate enough people, at some point we should start to see some effect on r because the virus will start running out of susceptible people to infect - we will move towards logistic rather than exponential growth. However, because Delta is so contagious, you would need a vaccination rate of about 85% with a 95% effective vaccine (like Pfizer and Moderna are, against the base strain, within a few months of the second dose) in order to reach herd immunity. Georgia is not getting anywhere near an 85% vaccination rate with Pfizer.
I did a very rudimentary estimation of Georgia’s immunity numbers for the next two months. Optimistically, there might be about 1.5 million Georgians who have been infected with covid - I’m just tripling the official number, given that previous experience (e.g. antibody surveys, random screening tests) tells us that official case reports get between one third and one half of cases. Pessimistically this could be as low as 1 million. There are now about 0.35 million people fully vaccinated. So right now we can estimate that 1.35 - 1.85 million Georgians have immunity to covid (and remember, this “immunity” is between 50% and 95% effective at preventing infection, depending on the source). I’m going to proceed with the most optimistic number - 1.85 million.
Supposing Georgia could administer 30,000 doses a day, you’d get about .45 million additional fully-vaccinated people each month. If previously-infected people get vaccinated at about the same rate as non-infected people, up to 40% of those people could be immune already - so vaccinations would add about .27 million to the immunity total. Given my worst-case projection (r = 0.9) we’ll see about .11 million reported infections by October 1st, which could be up to .33 million actual cases. Add these up - .27M new immunities through vaccination, .33 through infection - and get .6 million. Thus by October 1st, the best case scenario is 2.45 million people with immunity. Georgia’s population is about 3.75 million, so this leaves 1.3 million people susceptible - more than enough to sustain ongoing transmission.
In October, we could add another .27M people immune through vaccination, but only .18M new infections (again, assuming r=0.9), and so by November 1st, best case scenario is probably about 2.9 million people immune through infection and recovery, or vaccination.
Based on this estimate, the susceptible population would drop by about 21% by October 1st and another 19% by November 1st, for a total of 36% (remember these percentages are applied by multiplication of complements, not addition). So 36% is probably the upper bound on r reduction through vaccination and infection - and I want to stress “upper bound” because this projection is optimistic about the amount of infection-acquired immunity, and because there isn’t a 1:1 relationship between reduction in susceptible population and reduction in viral spread. That comes out to a decline in r of about 0.037 per week for September and about 0.032 per week for October. For reference, on a weekly basis, this is about an order of magnitude lower than the drop in r following the NPIs which came into force on August 14th (closed public transit, mask mandate, and bar/restaurant curfew). It’s also indistinguishable from noise - r swings of much greater than 0.037 per week for no obvious reason at all are very common. However, if we’re lucky, by November 1st, the cumulative effects of vaccinations/infections could potentially stop us from having another surge even if we remove the August 14th restrictions - assuming Delta is still the dominant strain at that point.
How might reality differ from this basic estimate? First, the rate of vaccinations could speed up. I’ve heard Georgian officials expressing a wish to vaccinate 80,000 people a day rather than 30,000. Obviously this would vastly increase the rate at which we vaccinate all willing and eligible people here.
Second, not everyone is willing and eligible. According to the latest NDI poll on Public Attitudes in Georgia, 47% of Georgians polled said they wouldn’t get vaccinated. About 1M Georgians are ineligible because they are under 18 [editor’s note: Pfizer is now available for ages 16-18 as well; this should not change the calculation much]. That means there’s a cap of about 1.5M people who are willing and able to be vaccinated. Note that if we did manage to do 80,000 shots per day, it would take less than a month to hit that number (given how many people are already vaccinated). We could then potentially hit 2.75M people immune by October 1st - but then for November we only add immunity from infection (estimated to be .18M) which gets us to 2.93M immune by November 1st. Note that this is not significantly different from the prior estimate, although the reduction in r happens earlier, which would make the entire curve lower.
Third, if people who already got infected (and know it) are less likely to get vaccinated, there might be less overlap between infections and vaccinations, meaning we might get more immunity. However, keep in mind that this estimate already assumed only one third of cases were picked up in official reports, meaning presumably most of the people with infection-acquired immunity don’t know they have it.
Overall, vaccinations (and new infections) don’t impact our forecast much, and to the extent that they do, the impact is mostly towards the end of the forecast anyway, which diminishes its impact.
NPIs
As I mentioned above, the August 14th restrictions did appear to have a noticeable impact on r. There was a noticeable drop in r starting a few days after August 14th - it was 1.29 as of the 16th, 1.27 on the 17th, 1.24 on the 18th, 1.18 on the 19th, and 1.09 on the 20th. As of August 26th it has dropped to 0.88 and stabilized. So it looks like the restrictions caused an overall decline of about 32% in about 12 days. For reference, it looks like our second wave lockdown, begun on November 28th, caused a decline of about 39% in about 21 days.
I say “it looks like” because there’s some doubt as to whether the correlation between lockdowns and later drops in infections are a result of confirmation bias: that is, a lockdown causes us to look forward to a reduction in cases, and so any subsequent reduction is taken as confirmation that the lockdown worked - even if that reduction wasn’t actually caused by a lockdown. What about the theory that waves in pandemics come about due to population dynamics regardless of government policy? What if a surge in cases causes people to independently restrict their own activities at the same time it causes the government to panic and institute a lockdown?
For the purposes of forecasting, it doesn’t matter much if it is the government lockdown, population dynamics, or individual behavior which causes a decline in cases. As long as these factors are correlated closely enough they’ll yield the same results. My personal take is that there’s enough evidence in favor of lockdown efficacy to believe that NPIs such as closing down public transit can and do have some impact on r, and the open question is how to balance the competing interests of rescuing the public health system from overload and saving lives on one hand, and the economic, social, educational, and other needs of a country and individuals on the other hand. In other words, I believe reasonable people might differ on whether a very strict lockdown is worthwhile, but I don’t think it’s reasonable to claim, given what we now know, that lockdowns have no effect whatsoever on viral transmission rates.
It’s also worth looking at the trend in r after NPIs are removed. Georgian NPIs began relaxing in February after the second wave - for example, on February 15th, schools opened for in-person instruction and restaurants were allowed to commence in-person service in outdoor spaces. The infection rate increased in Tbilisi from .84 on February 14th to .87 on February 21st and .97 on February 28th. However, in the same time period, r nationwide went from .9 on Feb 14th to .79 on Feb 21st to .85 on Feb 28th. Both nationally and in Tbilisi, it was March 14th - a month after NPIs started relaxing - when r rose above 1 and cases started rising again. On the other hand, after the third wave, cases started rising again almost immediately after NPIs were removed - the outdoor mask mandate was dropped at the end of June, curfew was dropped on July 1st, and by July 4th we were already clearly in our fourth wave.
Here it’s worth examining whether the removal of NPIs and the subsequent increases in r are even correlated at all. It looks to me like waves 3 and 4 were enabled by dropping NPIs, but were caused by surges in Alpha and Delta cases, respectively. So while I think that imposing NPIs quickly and significantly depresses r, it’s not quite as clear that lifting them quickly and significantly increases r.
High-transmission events
Throughout the pandemic, concerns have been raised over events which tend to produce large gatherings. Holidays during which families typically congregate - like Thanksgiving in the US, and Christmas in many Christian countries - cause concern that increased mobility and increased interaction will lead to a surge in cases. Other events, such as the Sturgis Motorcycle Rally in South Dakota, have been cited as the cause of subsequent large jumps in infection rate. On the other hand, Lollapalooza produced virtually no spread, perhaps due to its stringent safety protocols.
In Georgia, the Easter holiday has caused great concern in both 2020 and 2021. My prior analysis suggests that Easter 2020 did not cause a significant increase in cases - there was a small increase, but it appears that the NPIs the government had in place offset any major increase, and in fact r went down after Easter. Easter 2021 allowed the government to implement a soft lockdown which was billed as a “holiday” and seemed to reduce the infection rate enough to take us out of the third wave.
Finally, there were concerns raised over parliamentary elections on October 31st, 2020. The election was conducted with mask and distancing requirements in place and my impression was that compliance was relatively high. Five days after the election, we see r start to increase from about 1, reaching about 1.5 by November 10th, before starting to decrease again. This seems like a clear indication that elections were a superspreader event which drastically, if temporarily, increased the infection rate.
However, the data and trends around this time look suspicious in the context of the overall trends. Here’s the trend in r, where it looks like there was an unusual drop in cases right around election time, followed by a correction back to trend after elections - where these changes in r look a bit like random fluctuations.
Here’s the rolling 7-day case count for the same period. Again, it looks like there was a little dip right around election time, and then a correction back to trend.
Note that this dip looks a bit starker and more obvious in the context of the entire pandemic:
Without understanding what caused the dip, I’m not at all confident in saying the elections caused the subsequent surge.
Finally, if you disaggregate the numbers and just look at the daily new cases, you see the increase in reported cases actually began on October 31st and leveled off right around November 6th-7th, which is when you’d expect to see cases rising if the surge were really caused by an event on election day. Daily numbers are noisy and not good for projections, but I think in this case they help show that the “election bump” hypothesis isn’t a great fit for the data.
All this is to say, if supposedly high-transmission events - Easters, elections, etc. - are really having a significant and lasting impact on r, it isn’t clearly shown in the data. I could try to make some assumptions about NPI impact, subtract it out, and see what’s left, but I think this analysis would be misleading given that NPI estimates are extremely uncertain and lack the precision necessary to detect the effects I’m looking for.
What I can say is that the government has been very responsive to these events in the past - implementing NPIs in response that have probably drowned out any impacts of the events themselves - and that in itself tells me to expect similar measures around the time of local elections, which are due to occur on October 2nd, 2021.
Forecasting NPIs
My analysis above suggests that NPIs will be the dominant factor in determining the course of the pandemic over the next two months in Georgia - more important than vaccination rates, elections, or any other events or factors.
On August 27th, I wrote:
Tikaradze saying cases expected to be in decline in October. Only guarantee of that is if there's already a plan to extend or increase restrictions. I wouldn't expect her to go out on a limb and say this if that's not the case.
As I’ve said, there does seem to be a big lag time between dropping NPIs and a rise in cases - at least a month, usually - so it’s possible they could drop NPIs in mid-September and still be seeing declines throughout October. But Georgian officials have been very conservative in terms of making forecasts like this and this experience tells me that Tikaradze is aware of a plan to extend restrictions at least until elections and possibly for a time afterwards. This would make sense given Georgia’s responses to previous potential superspreader events.
I’ve also stated above that the earliest feasible time for the country to meet benchmarks to open schools would be mid-October. Keeping schools closed is technically an NPI, especially given that now our unvaccinated people are disproportionately children. I think it’s reasonable to predict, therefore, that we’ll have school closures and some other restrictions at least until mid-October.
If the NPI situation probably won’t change drastically, vaccinations won’t have a big effect on r, and elections won’t have a big effect on r, then I think the most likely scenario is actually that we’re looking at a fairly straightforward steady decline in cases - probably somewhere between the yellow and orange curves in my first graph.
On the other hand, currently the restrictions on public transport are set to expire on September 4th. This could have no immediate effect. It could be offset by different NPIs - perhaps a reinstatement of curfew - or increased enforcement of existing regulations. Or the transit closure could be extended. I’d say there’s a very small chance that this issue ends up pushing r upwards, but I doubt it would push r up much over 0.9.
Conclusion: Assigning Probabilities
Consider again the initial graph:
In order to go above the orange curve, the country would need to drop current restrictions, and that would need to cause a relatively quick resurgence of cases, or there would need to be some unprecedented superspreader event. I view this as quite unlikely, so I’m assigning it a probability of 15%.
In order to drop below the yellow curve, either restrictions would need to be tightened, or we’d need more immunity than my estimates, or there could be some kind of seasonal effect (e.g. people go outside a lot because the weather is cooling off), or some other kind of population dynamic effect, like the one I hypothesized might be generally driving down cases after peaks, would need to take hold. This is slightly more likely than the above, so I’ll call it 20%.
Below the blue curve seems vanishingly unlikely, but I’ll round it off to 1%.
The remaining probability - 64% - goes to the area between the yellow and orange curves.
Of course it is possible for the actual curve to move between regions, but assume the probabilities refer to where the actual curve will sit at any given time.
I had meant to include longer-term forecasts in this post, but it has run long already, so I will have to defer those to a later post. Go ahead and sign up for my free emails if you’d like to be notified when that (and other) posts come out.
Well, I called it:
https://agenda.ge/en/news/2021/2477
Transport closures extended until September 13th.
Schools will work online until at least October 4th.
From the article:
"Georgian health officials have warned several times that they will not recommend in-person studies until new cases of coronavirus will seriously decrease and at least 80 per cent of school personnel are vaccinated.
The Georgian Education Ministry says that after October 4 in-person studies will resume only in cities and settlements where the infection rate will be under four per cent."