Do not be satisfied with a Covid-19 reproduction ratio of 0.9

There has been much attention on seeing the covid-19  reproduction ratio below 1.0, and an assumption in some quarters  that 0.9 is “good”.

In fairness Prof Whitty emphasised that much lower would be better.

It is true that at 0.9 the disease should eventually die out in a given population.

But if the disease follows the mathematics, then an initial 1000 cases will cause, during successive generations of infection, the following numbers of cases:

900, 810, 729, 656, 590 etc …. approaching another nine thousand cases  in total
The expected further cases for various values of R,, the reproduction ratio on the same basis, are as follows

R		Expected further cases
0.9		9000
0.8		4000
0.7		2333
0.6		1500
0.5		1000
0.4		667
0.3		429
0.2		250

The dramatic difference in further cases between 0.9 and 0.8 demonstrates the value of effective measures to avoid the spread of the virus..

While it is difficult to assess R exactly, do not let us be satisfied with 0.9.

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Mathematical note: Total number of further cases =  1000  * R /  (1- R)

This follows from : R + R**2 + R **3 + R** 4 +… (etc)    = R / (1 – R)  for R <1