In this talk I will overview some analytical insights into the virus from our work in Lithuania. We will cover three topics: dynamics of the virus spread throughout the country, our testing strategy, which focuses heavily on exploiting the dynamics of the virus and focuses on highest-concentration locations like hospitals and nursing homes. Finally we will discuss some mathematical difficulties that CV19 presents to modellers and forecasters. 1
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Hard lockdown for 4 weeks had a profound effect. Since then, incremental relaxation of the lockdown under country’s strategy has kept virus spread under control. 3
Masks remained the key part of daily lives. Especially, for high and medium-risk groups (high-contact people). Usage of masks reduces average viral-load, which in turn reduces average severity of the cases. Mask may not be bullet proof for protecting an individual from infection, but in definitely reduced the spread of the virus by an infected individual if they wear a mask. 4
We do not see increase in average mortality in the country, so we are unlikely to be missing a lot of severe CV19 cases with our testing strategy. 5
Looking at dynamics of the virus – we see three waves of decreasing size in the country. Two primary regions are driving virus spread. We can see the waves consistently across the regions as well as country level. 6
Similar pattern is seen across Europe, so we think Lithuanian dynamics are not something specific to the country, but rather something intrinsic in the virus itself. We think it is to do with average incubation period, but many things could be the reason. 7
We will analyse where the waves are coming from in the two epicentres of the virus: Klaipeda – the port city of Lithuania and Vilnius – capital of the country. 8
Comparing Vilnius City and its surroundings, we can see clear phases of about 4 weeks each: infection outbreak in the city, followed by outbreak in its surroundings, and then again in the city. 9
Similar phasing is observed in Klaipeda City and it’s surroundings, we can see clear phases of about 4 weeks each. We have had less cases in Klaipeda, hence the data is more noisy. 10
However, we can look at the peaks instead of daily average to see more profound phases: three peaks in the city followed by three peaks in its surrounding area shifted in time. 11
We see the pattern of spread and phasing largely geographically and through contact networks (relatives, co-workers etc). Here we see the evolution of CV19 along the major road connecting suburban town Nemencine with the capital Vilnius. The delay between outbreaks was about 1-2 weeks. 12
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Significant adjustment needs to be done to the numbers we observe through testing symptomatic cases to estimate actual number of infections. We did several experiments to answer the question: “When you observer the first case in a contact network, how many cases are actually there?” And the answer has consistently been order’s of magnitude, here we see example in one hospital where after we tested first 4 people positive and decided to test the whole hospital, the total number of cases was 40+, 80- 90% of them symptomless. Virus spreads in these fast accelerations. What this means in practice, the you cannot “run after” the virus, but you need to get ahead of it – a bit like catching a criminal. You need to try to see where it is likely to go next and then try to prevent/control that. The thing that complicates the matters of “chasing” even more is that PCR tests are very inaccurate for diagnosing COVID-19. If you get a negative PCR – at best it’s a coin flip that person with mild symptoms has not been a false negative. This also means that once you got an infection in a contact network in you may as isolate/lockdown the whole network without having to rely on testing. This is one of the core principles in our strategy. 15
Our testing was not random – we applied some version of rotation principle to test exhaustively hospital staff (and in some hospitals patients also). What we found during this testing that we would either find the whole ward/care-home largely infected or not infected at all. In the example above, in the tested hospital, we essentially observed that once we had a single case in the ward, there was a significant number of CV19 cases. 10x on average. 16
We also tested one town of 2800 people fully when it had a single outbreak of CV19. We performed PCR and serological testing simultaneously and found a very small PCR- detectable prevalence of the virus. 46 people tested positive for PCR and 63 for antibodies only, suggesting that it was not the first wave of CV19 that we caught in town – we probably missed one or two infection waves already before severe cases appeared. Essentially, this network-based spreading combined with very low “PCR-detectable prevalence” makes random population tests very difficult – they need to be very carefully constructed considering those aspects and general sampling techniques are likely to underestimate the prevalence. And knowing the speed of CV19 spread (10x+ from observed to actual) – detecting small prevalence matters as in 10 days could be huge. 17
Our strategy for control of CV19 under quarantine was heavily focused on testing staff and patients in hospitals – we believe that the key virus spread center is a hospital. Then later shopping centers, business centers, etc. also become such and we are expanding our testing there now, but hospitals and care homes remain key potential hotspots. 18
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We will now overview some high-level thoughts about mathematical treatment of COVID-19. 20
Ultimately, we need to make sure we are doing the right type of science when trying to understand something new. If it is new, we likely do not have enough data to make conclusive arguments. In Lithuania, we took a physics-style approach of constructing theories of the virus dynamics and trying to break them. We also treated all public models as such and tried to break their assumptions in also become such theory and practice. Unfortunately, most we were able to break.. 21
A lot of models that we see in the world make dangerous assumptions, that do not hold in many cases. 22
The big danger is a fat-tail distributions that are CV19 has a lot. Many people know about them, but not many people have intuition of what it means to deal with them. One example is symptoms: when you have flu, whether you are 5 or 75, you will probably have fever. This is not true for CV19 – probability to have fever is heavily shifted to the “right”. Incubation period is another example. Let’s walk through this. 23
A very basic observation about these type of distributions is that Median may be very different from the Mean. And this is very dangerous – you essentially need to consider both and also look very carefully at the underlying data to understand the mathematical properties. 24
One example is paper establishing that median incubation period of CV19 is 5 days. It has been influential in setting policies worldwide, but knowing this is a fat-tail distribution – mean is very important as well. Specifically for incubation period, almost surely mean is higher than 5 (in the NECSI recent paper they modelled it has 8.6 as a fat- tailed Weibull distribution). One of the intuitive reasons why average incubation is higher than the mean is that the lower is person’s viral-load exposure, the lower is incubation period. In summary, we need to be very careful when interpreting scientific results and make sure we read the limitations and assumptions very carefully before making decisions. Conclusions are always caveated and one need to understand the caveats and implications of additional risk. 25
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