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Coronavirus Mathematics?

By July 20, 2020 September 6th, 2021 No Comments
Aeroplane chained by Covid

Mathematics is not political. A startup CEO should never be political, I tell myself, and indeed this entry is not political. I agree with everyone on some things. God or no God, mathematics of 1+1 is always 2, and whoever says otherwise is selling something.

The world today is divided between those who understand mathematics and those who do not. Those who understand mathematics understand that Coronavirus-type stochastic processes (even with 10% chance of contracting from close proximity with a sick person) are exponential, and controlling that contracting chance (bringing down 10% to 5% for example) results in super-exponential decrease in the population’s speed of contraction and is the difference between 10% mortality and 1% mortality.

Do the math, and you find that a delayed-observation process such as CoVid-19 requires you to act to contain things two months ahead of when they happen. If you act only when you see 10,000 sick people per day (e.g. Florida), then you’re going to see 100,000 sick people per day, with close to 1,000 people dying per day.

Those who do not understand mathematics say “Chances of it happening to me are very small, so why are you closing all those shops?” What they don’t understand is that if people do not wear masks and are close to each other then the mortality rate becomes 10% (see New York). So sure, you would be fine and likely won’t die, but the country would lose 10% of its people.

So I’d rather assume that you do not understand this math. The alternative is that you understand it and prefer that 10% of the people die. Surely you do not think so.

Hmm?HMMmmmm… Hidden Markov Models in action

On April 9th 2020 I asked a friend of mine for her estimate of how many people shall die by end of August in the US. I told her there were already 15,000 people dead. She said that by August it would be 40,000 people at most. I told her I believe 50,000 before end of April. On April 29th the number of deaths from CoVid-19 and its complications passed 60,000 people in the US.

My friend is highly educated and working in finance. Many economists gave lectures to top banks in mid April claiming that there would be at most 40,000 dead people in the US by end of August (at the time of writing of this entry I predict the US shall pass 200,000 dead people by end of August — the number right now is 143,000). How could my friend and her colleagues be so wrong?

The reason seems to be that financial analysts are used to processes where reality is visible or at least current: S&P information from a month ago is almost useless, and the AI models that analyze stock prices and news information are non-explanatory models that do not look this far back in time.

In reality many processes are at states that are not visible right now. A known mathematical tool used in Artificial Intelligence (AI) and Cyber Security is Hidden Markov Models (HMMs). Invented over 100 years ago, they model processes whose state is not visible (how many people are right now sick with CoVid-19?), that evolve stochastically (I was at a party with another sick person, what are the chances I got sick?), and whose state becomes visible only upon testing with delay (how many people are sick without symptoms yet and shall develop those symptoms?).

Methods in AI were developed over the past 30 years that can capture this pandemic’s behavior more precisely than the simple function fitting used throughout economics and finance. These methods are rather basic, and most computer-science majors know them these days. It is time that those who have important decisions in their hands know those basics.

A howler to my colleague DJ Patil and his list of to-do’s, including his institute for Data. May that data and institute be objective and a-political.


Written by Eyal Amir
CEO Parknav

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