Exponential growth

Just compare the two pictures:

Fear over freedom: Here’s what the doom-laden government graphs didn’t show us (telegraph.co.uk)



Why these two figures? Trying to argue against – otherwise quite mild – restrictions implemented by the English government, The Telegraph is falling into an exponential growth fallacy, illustrated by the second figure.

The problem is of course associated with the different perceptions of the exponential growth, depending on the current level. But this attitude can be quite deceptive – as time goes on and the spread is not controlled, the numbers will start growing faster and faster. At some point, the epidemic will be unstoppable.

There is of course a way to avoid this problem with different perceptions at different stages of exponential growth. A logarithmic transformation turns exponential growth into a linear one, allowing the policymakers to make appropriate decisions.

The period from July 2020 onwards has three examples of exponential growth in the UK data, as illustrated above. At each time, the decision to respond has come late. It was quite clear that the numbers were growing exponentially even from late August 2020, but the decision to lockdown was only taken on 22nd September. The next wave started on 10th December, but the post-Christmas lockdown came on 26th December. The spread of the Delta strain became obvious from 19th May onwards. This time the government has only delayed the further relaxation, but no additional measures have so far been introduced to combat its spread in schools.

Essentially, the nature of virus spread is that any action to stop it needs to be implemented as early as possible. With the Delta strain of SARS-CoV-2 spreading exponentially in the UK we are probably already at the stage when it is becoming too late to stop the rapid pandemic spread.

It is true that the numbers are still much smaller than in March 2020 or January 2021. It is also true that with vaccination the growth will probably slow down soon and the epidemic will peak at lower numbers.

But it is also true that had we protected the borders, had we had a properly working test-trace-isolate system and had we acted earlier to prevent the spread, we could have avoided the illnesses and deaths of many people.

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