Skip to content
Join our Newsletter

Herd immunity boils down to hard math

One of the strange aspects of being isolated is I am watching television programs I wouldn’t normally have time to watch. One was a nature documentary on a sea mount off the coast of Ecuador featuring the narrator discussing fish schools.
col-whitcombe._7312019.jpg

One of the strange aspects of being isolated is I am watching television programs I wouldn’t normally have time to watch. One was a nature documentary on a sea mount off the coast of Ecuador featuring the narrator discussing fish schools.

When being attacked by sharks, dolphins, sea birds, and other predators, the fish will school into a swirling tornado. The narrator pointed out the several advantages of such a strategy: it confuses predators by making the fish look like a single bigger organism, it makes it difficult for a predator to pick out a single target and it provides a form of herd immunity. Essentially, by bunching up, most of the fish will survive and only a few will be sacrificed to the jaws of, say, a hungry seal.

Herd immunity is a term which has crept into our lexicon over the past few years. With the recent outbreaks of measles, public health officers have worried about the loss of herd immunity among the general public due to the refusal of many parents to get their children vaccinated. Unfortunately, some very bad information has been passed off as “the truth” about vaccines resulting in children suffering and dying.

With respect to infectious diseases, the idea behind herd immunity is that if enough members of a population have antibodies to the pathogen, then there will not be enough people infected to sustain the disease. The R-zero value will be low enough the disease will not spread. This generally means a R-zero value of less than one – that is, each individual with the disease is infecting less than one person.

It is not too hard to follow the math with respect to R-zero. It is above one – say  two – then the first individual infects two others and they, in turn, infect four who will infect eight and pretty soon you have an pandemic. 

If you consider 2 raised to the 30thpower – 30 generations of contact – leads to over 1 billion people infected, it is easy to see how quickly a disease can get out of control.

But with an R-zero of less than 1, a disease dies out. For example, if 100 people have the disease and the R-zero value is 0.5, then they will infect only 50 people who will in turn only infect 25 who will infect 12 or 13 (actually, 12.5 but it is impossible to infect half a person!) and so on until there are virtually no cases of the disease.

Herd immunity is a way of keeping the R-zero value low. A contagion needs a receptive host but if the majority of the population is immune to the disease then R-zero will be very low. Few people will catch the disease and it will essentially die out.

There are many diseases that used to affect us in the past – the mumps, measles, rubella, small pox, and such – which have all been effectively eradicated by the use of vaccines to generate herd immunity.

In the case of COVID-19, governments of the world are betting on a vaccine offering immunity to a large enough portion of the population that the disease will go the way of the dodo. It is the hope we all have for a return to a normal life, whatever that might be.

But there are many caveats – questions for which we do not yet have answers. Indeed, some of the answers we thought we had are turning out to wrong. For example, the disease has a very long tail. It appears the time between contact and developing symptoms can be a lot longer than originally thought. And no one really has a good handle on morbidity rates yet, nor on just how many people are actually infected and how many are asymptomatic.

There is much that isn’t known and in the middle of a pandemic, it is hard to tell people it is going to take months to fully understand the virus. We need answers. Further, developing a vaccine in a matter of months – before the end of the year – will require a heroic effort. Testing it will take time and if we are going to vaccinate enough people to achieve herd immunity, it has to be tested before it is put into general circulation. To achieve herd immunity for a COVID-19, with an R-zero of between 2 and 3, at least 70 per cent of the population will need to be vaccinated. That is a lot of people to try out an experimental vaccine on. 

Waiting for us to naturally develop herd immunity, as some have suggested, condemns millions to death. It would require 70 per cent of the world’s population to catch the disease and recover. That is 5.5 billion people and with a fatality rate of one per cent, it condemns 55 million to death.

So for now, stay home, stay safe and practice social distancing.