the math is kinda wrong fwiw @dsymetweets. Plot 1.22**n and 1.21**n. Notice that after another day or two with 1.21, your gain is erased. What you buy is not really fewer infections, but time.
(Also these are sigmoids not exp, so the slower rate does converge to the faster one)
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The same effect applies to a three phase model of suppression, see spreadsheet later in the thread. Rates 1.3/1.05/0.9 v 1.29/1.04/0.89 over each of three months.
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Replying to @dsymetweets @JeremyRubin and
(The sigmoidal nature of epidemic curves is not particularly relevant in this case - in the UK only a small proportion of the population are getting infected during first wave. But adjust the model if you'd like?)
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1.3**90 = 17,984,638,289 Which I guarantee is more than the number of people who will get sick in any case ;) This is exactly why you should use a sigmoidal to capture the upper bound.
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Replying to @JeremyRubin @dsymetweets and
Will take a look at your spreadsheet later.
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Right. It's an approximation of what's actually been happening, eg a month of 1.25-1.3x (depending when you start), a few days of around 1.05x then ongoing 0.8-0.9x.
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That is, what's roughly been happening in the UK as far as I can tell. The ~20% reduction still applies to a 0.01x change across that model. Compounding isn't the important part, it's the reduction across the each and every day of the time period, with early reductions accruing
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