Ro and Herd Immunity are Intimately Connected

by ukcivilservant

I have only just understood the intimate connection between R0 and herd immunity.  I offer this explanation to others who may have shared my ignorance.

If R0 is 10, every infected person typically passes enough virus on to 10 other contacts to make them ill – unless of course they are already vaccinated or otherwise immune

If over 90% of the population is already immune, every infected person will still pass the virus on to 10 others, but less than 10% – that is less than 1 of them – will now also become ill, and the illness will die out.  The perceived R, in other words, has become less than 1.

Measles is highly infectious.  Its R0 is around 15 which means that the illness will spread through a population if more than 1/15th (6-7%) of the population lacks immunity.  New births and deaths are constantly increasing the proportion of those who are not immune.  That is why medics want to see most babies vaccinated, so that around  93-94% of the total population remain immune.

COVID-19 R0 appears to be around 3.  If so, the illness will spread quickly if more than 1/3rd of the population lacks immunity.  But herd immunity might be achieved at around two-thirds (67%)  of the population – though only if an initial infection confers long-lasting immunity.  If not, then we can probably only achieve herd immunity through repeated vaccination.

Further information about epidemic theory is here.

Martin Stanley

Editor Understanding Government