Doubling Time, by James Thompson

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Arnold Weinstock, a British industrialist, once said “I’ve forgotten what the 7 wonders of the world are, but the 8th must be compound interest”. Under his cautious guidance General Electric became a great UK company. Under his successors it went bust. Some problems compound and need to be nipped in the bud.

A respect for compound interest is not new. The origin of the story may even pre-date 1256, where it is presented as the request that payment be made in the form of a single grain of wheat being placed on the first square of a chessboard, and doubling thereafter. The answer is 18 big ones, quintillions. 10 to the power 18.

These answers are counter-intuitive. Most people prefer a million dollars right now rather than a penny doubling every day for a month. Exponential growth comes as a surprise. Another example, given in various forms, is the lily in a pond which doubles every day. If the pond is full on the 60th day, on what day will it be one-quarter covered?

Most people tend to think in linear terms. Perhaps this is because payments by the hour or week or month tend to be linear, and that is how most people have to judge these matters. Handling investments is usually only done by a minority.

The spread of an infectious disease follows the same exponential pattern, hence the deep interest in the doubling rate of coronavirus infections, used as a shorthand for the growth in number of cases.

Imperial College has been running simulations, and also running into criticism for them. The code is written in thousands of lines of C and is undocumented, the lead researcher explains, in a short break from running more simulations and recovering from the infection himself. “Tut tut”, say the critics.

This is silly. If people had been interested in this problem years ago, they could have done the work themselves, documenting and publishing their code. There must be lots of programs out there against which the Imperial College simulations could be compared. However, there is certainly an odd assumption that intensive care beds are the key variable to be managed, unless one knows the success rate of such facilities with respiratory problems in mostly old aged patients. As the triage guidance gently puts it, one must consider if the outcomes are ones that patients would be happy to live with. Survival rates may not be very much improved among the severely sick elderly. Some estimates are that ventilators saved only 3% of such cases.

Now, there is indeed a simulation from the University of Oxford Medical School, against which the Imperial College predictions can be compared.

Commenter Philip Owen says:

This is far less apocalyptic than Imperial College. To be fair it is recent and models SARS2/Covid-19. It suggests that as high a proportion as two thirds of the UK population has already been infected! The core suggestion is, that many of those testing negative have in fact already had the disease in an exremely mild form. Young and socially active got it first? In Italy, they speculate that as many as 80% of the population already have been infected.

The inference is that SARS-CoV2 infection will be largely over in 3 months from the initial cases coming to attention. This is far less dramatic than the Imperial College model (based on flu). It is much more consistent with the cruise ship data except that the people testing negative for the virus, in large part, had already had an asymptotic infection that had been cleared by the body before testing.

I need more time with this, but it would be good if modellers all followed the same protocol in the summary of their methods, so that we could compare their assumptions in a common format. They make many disclaimers about the error terms in many of the figures, and call for antibody testing to see who once had the virus and may now be immune, for a while at least.

We need more competing simulations, and more debate about underlying assumptions.

Incidentally, this crisis may change health services for the better, by ensuring that all consultations are online initially, which should be more efficient, and less conducive to cross-infection. Add in some good quality video and remote health monitoring and there could be a more effective delivery of medical care, with face to face interventions being focussed on key cases, while the worried well are directed to other, less expensive, resources.

This will not happen seamlessly. Currently pharmacies are struggling to meet demand, likewise companies delivering medicines direct to patients at home. Pharmacists have turned down people calling to collect prescriptions on the ground that they had already ordered them to be delivered. The companies themselves deliver very late, so patients short of medication are in a Catch 22.

Also, quarantine is stressing delivery services, which require two hour waits, and politely restrict those endless additions to an order which were possible Before Corona. However, money is pouring into these services, and some shoppers may decide to give up old style food shopping and get back to home delivery, a middle class habit in early 20th Century Britain.

After Corona, before we ever board a plane again, security checks could also include basic health checks, and anyone with a high temperature, or even with a cold, could be denied access. Might help us all in a big way.

Currently, an exhibition centre in East London is being converted into a 4000-bed overflow hospital for London. It has very high ceilings, and will certainly be spacious. They may even have sufficient toilets, and kitchen space. Unless they have excellent staff and equipment, many may prefer to take their chances at home.


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