Review of mathematical model

Review of mathematical model
----------------------------

Let's start with an important observation: An infected person only becomes a "case" once they have tested positive.

So the percentage of infected people being detected (becoming cases) obviously depends on how much testing is being done. The less testing being done, the less cases there will be.

In particular, in the UK there are at time of writing only 10000 tests being carried out per day, so there can be no more than 10000 new cases per day, no matter how widespread the infection actually is. Be aware of this when you read the official statistics.

From there, realise that if the number of new cases appears to be slowing down from an exponential growth, to something more linear, this could simply be a reflection of the testing capacity being saturated. Not necessarily that the infection is spreading less aggressively.

So case numbers can easily be misleading.

On the other hand, South Korea have been testing most of their population. So most of the people there who are infected are being counted as cases. It is considered the "gold standard" of testing for this reason.

---

One figure which can't be as easily hidden as coronavirus infected, is coronavirus deaths. Postmortems usually reveal if a person died of coronavirus. Although:

1) If the influx of dead is too large to handle, then these postmortems may not be carried out adequately, and the cause of death may not be proven as coronavirus. This is actually distorting the official figures in some countries, such as the UK which openly admits that it is not testing deaths outside of hospitals, so they are not being counted as coronavirus deaths.

2) If a country chooses to hide truths, then the number of coronavirus deaths might be deliberately obfuscated. I would hope that the so called first-world countries are not in the category, though both France and UK have openly admitted to not counting elderly people dying in care homes from the virus, even where they are strongly suspected to be coronavirus deaths.

3) There may be additional bias in how data is presented/interpreted. This can be either accidental (hope/optimism), or deliberate (misdirection). Sudden jumps in case numbers have been dismissed as being "only because of more testing being carried out", and "only because some numbers are being counted when they weren't before". Then at the same time reduced growth in case numbers is celebrated, even though it could just be a result of testing capacity being saturated, or changes to testing policy. Any change to how data is generated and gathered creates an opportunity for biased interpetations and misleading explanations.

Hopefully the coronavirus deaths going uncounted constitute a small percentage, but who knows. Some experts believe as many as 50% of coronavirus deaths are going uncounted. [1]

---

From South Korea's statistics [2], we can at estimate a running mortality rate of the virus:

  9976 cases in S.K. as of April 2nd, and let's assume the vast majority of infections are being detected there.
  169 deaths in S.K. as of April 2nd => 9976/169 = around 60x as many currently infected as there are currently deaths.

This is of course a lower bound, because some infected persons may have slipped under the radar of South Korea's testing regimen. The actual ratio may be higher than 60x, and it may be slightly different in different countries, for various reasons. But it is nonetheless a good estimate we can apply to other countries. ie, We can use it to estimate the number of infected in any other country by multiplying the number of deaths there by 60.

For the UK, this works out as 2352 * 60 = around 141k infected, as of April 1st, of which 29k are cases (have tested positive). ie, only around 20% of infected persons being counted as cases.

This figure of 20% we have arrived at is fairly consistent with the government's own estimates [3] that around 15% of infected persons require hospitalisation. (The logic being that given the current policy is to test only hospitalised persons, then only 15% of infected persons will be counted as cases)

This figure of 141k infected is also very consistent with the mathematical model I developed at the beginning of March, which forecast 68k-354k infected by April 1st. [4][5]

Repeating this with some other data points:

Data point      Official    Official     Estimated persons          My model predicted infections
                Cases       Deaths       infected (deaths x60)      (50% confidence intervals)
-----------------------------------------------------------------------------------------------------------
March 10th         383           6            360                  437 -       572   outside range
March 20th       3,983         177         10,620                4,992 -    10,747   in range
April 1st       29,474       2,352        141,120               67,811 -   354,087   spot on
April 10th      73,758       8,958        537,487              367,552 - 3,378,080   in range

In conclusion, my model seems to be holding up pretty well over a month later.

Even if coronavirus deaths are twice the official figures, (and so infected persons are twice these estimates), the model is still making reasonably good predictions of the course of the pandemic, comparing it with our current best guess of the current state of affairs.

references
[1] https://news.sky.com/story/coronavirus-government-close-to-lies-over-coronavirus-deaths-warns-expert-11972083
[2] https://www.worldometers.info/coronavirus/#countries
[3] https://www.theguardian.com/world/2020/mar/15/uk-coronavirus-crisis-to-last-until-spring-2021-and-could-see-79m-hospitalised
[4] https://pastebin.com/tRm6rgZ8
[5] https://twitter.com/_sorceress/status/1235584222364082177