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Corona Statistics, Corona uncertainty

There is a saying "It's an ill wind that blows nobody any good". The Corona pandemic certainly has been pushing statisticians into the limelight as well asgiving us really tough challenges. I was invited to give a talk on this topic to Leiden Science alumni. We used Kaltura NewRow and ... let me just say, next time the speaker and the organisers will both be able to do a better job.

But despite imperfections I'm quite satisfied with the result, which was a snapshot of recent and presently important statistical issues, see the slides of the talk and part 1 & part 2 of the video recording.

Epidemic Modelling

I covered a number of topics. The first, the only one I will go into here, was about the epidemic modelling done by RIVM-CIB, the Dutch version of CDC with our own version of Dr. Fauci. Their modelling is based on refinements of a classical model called the SEIR model.

You start with a lot of people, Susceptibles (S), who have never been exposed to the virus before. Add one Infectious (I) person, stir well. That person will start infecting people, who are thereby now considered Exposed (E); they are now *incubating* the disease. After some time they actually get sick and from this moment onwards they can make other people Exposed, who later still become Infectious themselves. 

What happens to the Infectious could be many things - maybe they die, maybe they recover and are now immune and will never be sick again, or maybe they are shipped off to a leper colony and are never seen again. One way or another, they are Removed (R).

There is a wonderful website where you can play with model predictions while varying the model parameters.
 

Process of infection

The roots of the model are stochastic: each individual who is Infectious has in each small time interval the same small chance of meeting *each* person who is Susceptible and thereby pushing them into the category Exposed. In each small time interval each Exposed person (who is by definition incubating the disease) has the same small probability of becoming Infectious. Etcetera. With these stochastic root ideas one defines a continuous time, time homogenous, discrete state Markov process, the state space being the vector of total numbers of individuals in each of the four states. Now one looks at the mean numbers of individuals in each state and note that they follow a system of ordinary differential equations. You solve the equations, and hey presto ...

In particular, the *expected number* of exposed persons will initially grow exponentially if and only if, at the beginning of the epidemic, one infectious person, on average, infects more than one other person. That's the famous R0, and government has to make interventions in society in order to reduce R0 to below 1. The whole herd immunity discussion too, has grown out of these ideas.

Problems with prediction

Well, The RIVM does realise that things are much more complex than this, and anyway, we now know that Covid-19 doesn't fit well into this framework at all. Still, most of the scientists working at RIVM-CIB come from an applied mathematics - differential equations background. Randomness and uncertainty are afterthoughts. Fortunately, tiny changes of model parameters produce widely different projections of where we will be in, say, a week, so it is easy to use this deterministic, evidently grossly oversimplified model, to show that we really can't say much about where we will be in a couple of days. It's like the weather.

For some hopefully entertaining anecdotes and some gems of wisdom, see the slides of the talk and part 1 & part 2 of the video recording.

Right now I'm working with some controversial French doctors on the controversial Hydroxychloroquine treatment - the anti-Malarial medication one which Donald Trump recommended and which a couple of his voters saw on the label of a bottle of fluid they had bought for treating their pond carp for some parasitic infection. They drank some and died.
 

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