May 8, 2020

# COVID19 Herd Immunity Strategy Makes No Sense

When watching COVID-19 news you have may have heard about the R0 number or **basic reproduction number**. This is how many people on average a person who is sick will infect given no intervention and no immunity in a population.

For COVID-19 this is 1.4–5.7. Perhaps more commonly mentioned is the R number, or more correctly Re, **the effective reproduction number**. This is how many people each person will infect once active measures have been put in places such as social distancing.

You can use these number to determine the size of the population which needs to be immune for the virus to stop spreading. If R < 1, then each person will infect less than 1 person on average which means the virus will eventually die out.

The number of people required for herd immunity is determined by:

`(R - 1)/R`

We can plug in some numbers for this. If R is in the upper bound, because we have basically no measures in place then R = 5.7.

`(5.7 - 1)/5.7 ≈ 0.82`

That means over 80% of the population needs to be immune to stop the spread of the virus. However if we can get the number down to say 1.4 we get this result.

`(1.4 - 1)/1.4 ≈ 0.286`

That means at R = 1.4, we only need 28% of the population to be immune for the virus spread to gradually die out. That is close to what New York has as of 27th of April 2020. Estimates from that time is 25%.

Getting to that number is then actually possible within a reasonable time. Getting a R < 1 is also possible as demonstrated by numerous countries which have achieved an R < 1 after lockdown measures.

That means a possible strategy is to let disease slowly spread until say 28% of the population is infected. At that point one can open up partially. As long as measures in place are able to keep R < 1.4 the disease will not spread.

This is a more practical approach than waiting for 80% of the population getting infected, which will kill a lot more people and risk overburdening the health care system.

## Why Push Rapid Herd Immunity?

This is what I don’t get about the people arguing in favor of letting COVID19 spread rapidly to gain Herd Immunity quickly. The argument is that this will save more people in the long run.

This argument makes absolutely no sense. If New York could get to 25% with immunity (or suspected immunity) within just around a month, we can afford to slow this down and get there slower. Lockdown got things under control in about 2 months, we can use a hammer and dance forward and edge towards 28% or whatever number works.

As immunity grows, we can have less strict social distancing rules.

If we move slow that means that at any given time the number of infected people will be small. Thus once we hit the magic R, we don’t need a lot of time for COVID19 to wind down.

Here is a thought experiment. Say country **A** flattens curve and keeps spread slow so that about 10 000 are sick at any given point, while country **B** aims for rapid herd immunity by letting up to 1 million be sick at any given time.

We can use *r* for the rate taking into account both social distancing and immunity. When *r = 0.5*, country **A** will experience number of sick and infectious drop to 5000 people after say two weeks (I am not sure how long people infect each other). After four weeks we are down to 2500 sick and infectious.

Now compare this to country **B**. After two weeks you are down to 500 000. After four weeks it is 250 000. It takes almost 1 million extra to wind down.

That means the country which choose flattening the curve get a lot less sick people before the disease stops spreading. That will save a large number of lives.

That is why the most sensible strategy to me seems like the hammer and the dance. The numbers may creep up over time. But as long as you have some social distancing rules in place at some point it will stop spreading.

## A Society We Can Live In

Such a society should be possible to achieve. It means we have to keep stricter rules on schools and workplaces. We may have to limit things like concerts and movie theaters. But we can still go to work, school, shop and go to hairdressers etc.

That is a livable society we can stomach until a vaccine or effective medication is developed.