The SIR model and importance of the R0 Reproductive Number – Coronavirus

Posted bydocbrsPosted inCoronavirus, Covid-19, Reproductive NumberTags:, , ,
Solving log(x) = R(x-1) for a family of R values

In the recent daily UK Government presentations, the R0 Reproductive Number has been mentioned a few times, and with good reason. Its value is as a commonly accepted measure of the propensity of an infectious disease outbreak to become an epidemic.

It turns out to be a relatively simple number to define, although working back from current data to calculate it is awkward if you don’t have the data. That’s my next task, from public data.

If R0 is below 1, then the epidemic will reduce and disappear. If it is greater than 1, then the epidemic grows.

The UK Government and its health advisers have made a few statements about it, and I covered these in an earlier post.

This is a more technical post, just to present a derivation of R0, and its consequences. I have used a few research papers to help with this, but the focus, brevity(!) and mistakes are mine (although I have corrected some in the sources).

 

Published by docbrs

After a career with several organisations, broadly in IT, I now have more time to follow physics (mainly cosmology) and mathematics again, as well as reviving my cycling, and having more time for skiing.
As I get older, I'm more relaxed about some things, and less patient with quite a few others! It seems quite random, but my interests and prejudices will show as I post more blogs, I suppose. I have used Twitter and Facebook for a while, but I have found 140 (or even 280) characters on Twitter too few to make points in a nuanced way (opinions on Twitter are VERY black and white, and sometimes downright offensive); and FaceBook, while I use it a quite a lot, isn't really a medium for debate.
So here goes with a blog, at last!