Note: My definition of Herd Immunity is the total % of the population who get infected once the epidemic has completely finished. Most people define it as just the % of the population infected once the peak is reached. This gives much lower figures – 60% rather than 90% !
When a new disease enters into a community without prior immunity it will spread if R0 > 1 . R0 is simply the number of people the first person with the disease infects before he/she recovers (or dies). If R0 < 1 then the disease fades quickly away and has no lasting effect, while if R0 >> 1 the faster the disease spreads. Avian Flu was an example of a lethal disease but fortunately for us had R0 < 1. People got infected by birds but did not easily pass it on to others before they died. As a result there was no pandemic, despite WHO warnings of one at the time.
In the UK there are 65 million people all initially susceptible to any new infectious disease arriving in the country. It is estimated for Covid-19 that R0 probably was around 2.4 in Wuhan. However for simplicity let’s consider a general case where some disease has R0 = 4 and that the infectious period is 5 days.
At the start of the epidemic one infected person arrives in UK and infects 4 others before recovering. These then each infect 4 others so that the infected population will increase as every 5 days.
It is probably only after ~1 month that anyone really notices that there is a problem, but by then the epidemic is already increasing “exponentially” out of control. However there is a safety catch. Eventually each new infected person begins to meet some of those also infected or already recovered, so now cannot pass it on to 4 new cases. The reservoir of susceptible people is quickly running out and R is now diminishing fast. It reduces to 1 at the peak of the outbreak and then falls dramatically as the epidemic collapses. The population is then said to have reached “herd immunity”, and the UK is afterwards immune to any new infections arriving from abroad. One interesting fact is that herd immunity is always reached before everyone in the country is infected. A percentage of the population will always escape any infection, but this percentage depends critically on the initial value of R0. Here are two examples.
Herd immunity is only reached after 90% of the population have been infected, but at least the epidemic ends much faster!
Governments can reduce “R” through social distancing measures, but this is a tricky process because to return to “normal” life infections would essentially have to drop to zero, perhaps through track & trace. Alternatively we could eventually reach herd immunity with maintaining R=1.2 but that would take 9 months, and even then may not be sustainable while infection rates outside the country remain at R=2.4. So In both cases international travel might still need to be controlled indefinitely.
The only certain way out of this dilemma remains either a rapid development of an effective vaccine, or a drug treatment which renders the disease no worse than a cold.