Delays in feedback: Learning to drive, brain waves and COVID-19

With the numbers of new COVID-19 cases in China diminishing by the day, China now faces a problem. How to get the country back to work, or partly back to work, or more back to work, without taking too many risks with the virus taking off again. The risk can’t be eliminated, except by shutting its borders altogether and eliminating the possibility of reimported cases, but it will likely look to find the best balance of productivity and risk. Basically, it’s successfully pushed stage 2 of an outbreak back into stage 1,  as Siouxsie Wiles puts it, and will want to keep it that way while still being productive as a country.

But changing the way that the outbreak is managed is problematic. The effect of a change in management won’t flow into the figures for several days. When we look at data for new cases of COVID-19, such as the Johns Hopkins site or the WHO situation reports, the ‘new’ cases that we see today are the result of infections caught several days (maybe even two weeks) ago. There’s a big time lag between being infected and being recorded as a case. So, for example, we can expect to see Italy’s numbers to keep rising for several days to come, before (hopefully) they start to decline as a result of the country’s lockdown.  We mustn’t jump to the conclusion that the policy hasn’t worked on the basis of what happens in the next couple of days. It will take longer than that.

The same caution has to reply in reverse, however, as China now faces. One could imagine the following scenario. (I highly doubt this will happen, because the Chinese authorities won’t be this careless):

  1. On the basis of some really low numbers of new daily cases (zero in most provinces – see Table 1 of the WHO situation report for 10 March) there’s a small relaxation in the movement, socializing and working restrictions.
  2. A week goes by, and the new daily cases are still showing zero (because the flow-on effect of 1 hasn’t taken effect yet). It’s looking good, so there’s more relaxation in the restrictions.
  3. Another week goes by, and the daily new cases are low (but not zero). Action 1 has now had an effect, but not a big one because the relaxations were small.  Since the daily cases remain low, more relaxation follows. Yay! We’ve beaten this and everything’s heading back to normal, we think…
  4. Next week, and now action 2 has taken effect. And now daily cases are on the rise (!) but they’re still fairly small. Perhaps action 2 was a step too far?  It’s unclear, so there’s no new change in policy.
  5. A fourth week goes by and now the impact of the over-relaxation action 3 hits. And the figures are taking off again. But let’s not panic. We’ll tighten the policy just a little (back to 2).
  6. After the fifth week new figures are rocketing upwards. The policy gets tightened again…
  7. And we are back where we started.

We see that applying changes too quickly has resulted in cyclic application of restrictions. We relax the restrictions too hurriedly, then are forced to reapply them quickly.  The policy is unstable.

In physics, any delay in feedback tends to cause oscillations. By this, we mean that any changes to stabilize something, that have a delayed effect, will cause a cyclic behaviour. If you’ve ever tried to steer a large boat, you might have found yourself zigzagging along rather than keeping a straight path. It takes some time for the path of the boat to change when you turn the wheel or push or pull the tiller. You try to steer, and seeing that your action hasn’t had an effect, you increase it. But when the impact of it happens, you find you’ve increased it too far. You’ve steered far too much, and now you have to steer back again. But again your action the other way doesn’t seem to do anything, so you increase it. And you end up going too far back the other way. And so on. Bunnyhopping a car as you are learning to accelerate smoothly is another example of this – the effect of your shoddy clutch and accelerator work is slightly delayed, and as a result we end up with a cyclical acceleration.

Delayed feedback between the cortex and the thalamus in the brain is also thought by some to be the cause of the very cyclical ‘alpha oscillation‘ seen on the electroencephalogram (EEG, or ‘brain waves’, that is voltage recordings taken from someone’s scalp). The cortex communicates with the thalamus (deep in the brain) which communicates back to the cortex. The effect is a modulation of the cortical activity, but there is a delay. And this can cause an oscillation when the cortex isn’t doing much else.

Anywhere in physics where the effect of an action is delayed is potentially dangerous territory. COVID-19 is no different. If we want to know the effect of an action, we have to wait.





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