The Herd Immunity number explained

Unsurprisingly it was  the work of two Scottish mathematicians McKendrick and Kermack, who developed the S-I-R model that epidemiologists work with when deciding policy settings for pandemics. (S= Susceptoible, I= infectives and R= removed). Of course the maths has improved enormously since they developed the model in the 1920's to explain why pandemics behave the way they do. And the maths is not always intuitive. eg. Ebola  for example, would have affected 58% of the people in the world had no action been taken following an outbreak. Whereas polio would infect 99% of the world's population if no action was action following an outbreak.  It all depends on various factors rolled into a mathematical numbers including Ro.
So what vaccination rate do we need to achieve herd immunity from COVID?
This depends on several factors but Ro is the most useful. The Ro factor is the basic reproduction factor and depends on (i) size of population (ii) rate at which susceptibles become infected and (ii) rate of recovery or death from the disease, but also social structures etc have impacts on this important figure. 
You may have seen a number called Re quoted in the media. Re is the average number of secondary infections caused by an infectious individual at a given point in  an outbreaks progression. By definition if this is less than 1 then the contagion is reducing. But scientists when they look at herd immunity have also shown that if 1/Ro of the population is left unvaccinated and unprotected then there is a relationship between Ro and Re that achieves an Re of less than 1 for long periods of time and then herd immunity will be achieved. (still with me Davo?) 
Of course the factors Ro and Re do not reflect the severity of the virus on humans. But that's the maths. 
Scientists are still evaluating the Ro number but its likely to be about 5-6 which will mean more than 80%  of the population will need to be vaccinated to achieve herd immunity. 
And here's a salient bit of history from the UK. In 1996 the MMR or Measles, Mumps and Rubella vaccinations had reached 91.8% of the population - close to the herd immunity rate .....when a doctor (now deregistered) prompted the ant-vax campaign by suggesting (wrongly) that MMR vaccine had a relationship to Autism. Consequently MMR vaccination rates dropped and in 2018 Europe had 60,000 measles cases and 72 fatalities. Tragic. But encouragingly vaccination rates are now improving. 
Fortunately from Rotary perspective the success of the  polio campaign  is a great example of what can be done with the right vaccine policy and implementation. 
From: The Maths of Life and Death by Kit Yates. Curated by a certain scribe.