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I'll try, but my mathematical knowledge only goes as far as A-Level Further Maths - which is farther than many but not as much as the gentleman in the thread https://twitter.com/colourfulsevens/status/1355439454018805760?s=19
So, under conditions of pretty consistent lockdown, you would expect to see a consistent rate of decay in the number of new covid cases. It should get lower at roughly the same rate. As @BristOliver says, this shows up as a roughly straight fit line on a logarithmic (log) scale.
Here is what that would look like, more or less. Smooth up, smooth down. It's more complicated as that but this helps visualise it. https://twitter.com/JamesWard73/status/1355304169280856070?s=19
However, as you can see from @BristOliver's plot here, the case numbers are actually beginning to decline faster than you'd expect from that trend — see how the points diverge from the trend line. https://twitter.com/BristOliver/status/1355187197180334084?s=20
This is introducing a quadratic into the trend: in simple terms, the rate of decline is accelerating rather than staying constant, so the trend line curves on the graph rather than being straight.
Why? Something must be happening to speed it up, no? Vaccines?
Well, @JamesWard7 notes that the same curve in the graph could be produced not by vaccination, but by one day of socialising producing a sudden, sharp spike in case numbers. Remember the one-day return to school? https://twitter.com/JamesWard73/status/1355304951568879619?s=20
This and his previous tweet show that the effect could be almost illusory - what looks like an accelerating decline is the effects of one bad day shaking itself out of the data https://twitter.com/JamesWard73/status/1355306543038783488?s=20
Complicated, but this shows up in the age data, too - the effect is stronger among those demographics most exposed to the ill-fated school return. https://twitter.com/JamesWard73/status/1355312170330972167?s=20
So, it's bad news? Not entirely. There's still a quadratic curve among the over-80s. One day of school reopening wouldn't have been enough to expose them to their grandchildren.
And as @JamesWard73 says: https://twitter.com/JamesWard73/status/1355313884169728007?s=20
And as @JamesWard73 says: https://twitter.com/JamesWard73/status/1355313884169728007?s=20
Hope this is helpful @colourfulsevens
