Levels of immunity

One of the key questions underlying the future course of the coronavirus epidemic is the level of immunity in the population. In other words, it is the proportion of people who have been through the disease, either with or without symptoms, who are now immune to it, at least for some time. This proportion is very important, as it determines the famous (or infamous) “herd immunity”.

There is a huge effort now on trying to establish this level. It is not an easy task, as there is no simple test that can tell us that we had the disease and that we are immune. There are also logistic difficulties in how we can measure this level across the whole population. There are different methods and the most popular involves taking blood samples and testing for the presence of antibodies. These are chemicals that the body uses to fight off the disease, and if you have had COVID-19, you would have the antibodies in your blood (this is all very simplified here).

There is now an increasing number of such studies available and a couple landed in my inbox this morning. There is a study from a single hospital at in Wuhan; more studies are summarised by an article on Bloomberg web site (which otherwise concentrates on the fatality rate, about which I will write a different post).

The study in Wuhan, which was the epicentre of the pandemic, suggests about 10%. The city of New York shows 21.2% while the State of New York is about 13.9%. In a study from Germany, we are seeing the levels of 14% and from Switzerland, 5.5%. The important thing about these studies is that they attempt to test more or less a representative group of the population so that we can get an idea of what actually is happening outside the hospitals and care homes.

There are two lessons from these very early studies. Firstly, the numbers point to a substantial epidemic. About 20 million people live in the City of New York; assuming a conservative proportion of 13% holds for the whole population (i.e. that the study was representative), we get 2.6 million people who were so far infected. The whole New York State currently has 300,000 reported cases, so the under-reporting is about 8:1. In other words, for every reported case, we see 7 unreported ones. This is actually not too dissimilar to such diseases as flu (both pandemic in 2009-10 and seasonal) and measles before the vaccination.

Secondly, these numbers are very low for “herd immunity”. Given what we know about the rate of spread of the SARS-CoV-2 virus without the social distancing measures, we need about 50-70% of the population to be immune to stop the spread and re-emergence of the disease once the lockdown is removed.

Why is it so important? The epidemiological theory can be used to explain the relationship between social distancing, immunity levels, and the reproduction rate which measures how fast the virus spreads in the current situation. These three factors are closely linked. The more social distancing measures we apply, the lower the rate is and the lower the “herd immunity” is required to stop the disease from spreading. However, if we relax the distancing, the rate shoots up and so does the “herd immunity” level.

At the moment, most countries implement some forms of social distancing, reducing the basic reproduction rate to close to or below 1. If the rate is below 1, the disease will slowly die out regardless of the immunity levels, but only a small proportion of the population will become immune. But even if the rate is only slightly above 1, once we reach the appropriate immunity level, the disease will start to disappear. New Zealand is now close to local eradication of the virus by having reduced the rate very early and keeping it below 1. South Korea uses a different method but the underlying mechanism is similar, i.e. the reduction of the rate. In contrast, Sweden appears to have reduced the rate much less but is hoping to reach the “herd immunity” level corresponding to its current social distancing measure.

However, all these countries at some point would need to relax the lock-down measures. This will result in an increase in the effective reproduction ratio. Countries like New Zealand hope that by having reduced the local number of cases to zero or almost zero and by having implemented a stringent border control, they can cope with the increased rate. Such a strategy is risky, as shown by Singapore (and mainland China) which after a successful eradication campaign are now seeing an increase in imported cases. Another strategy is to rely on “herd immunity” to reduce the potential of the disease to spread, and Sweden appears to be following this course. This is risky as well, as it potentially leads to a lot of otherwise avoidable deaths. The UK and the US are still far from any of these considerations.

The overall message is that unfortunately, the social distancing measures will be with us for quite a while, but given the underreporting, perhaps not as long as we might have feared.

New article

I have just published a new article on The Conversation, titled, Coronavirus: how to use a vaccine when it becomes available. In it, I say:

As we are waiting for the coronavirus vaccine, it is important that we consider now how it can be used in the most cost-effective and publicly acceptable way. We need to know how to balance the demand for herd immunity with the protection of individual rights.

To me, this is the key message from this article. Nothing will work if people are not on board.

Positive and negative

I have been doing a lot of data analysis and modelling recently, drawing lots of figures like the ones in my previous post or below. I enjoy my work (although it can be very frustrating at times) and I enjoy maths, statistics and numbers (I know, I am a sad person). So, I have actually been enjoying working on coronavirus data.

Until something hit me yesterday. The UK Prime Minister is in intensive care with the virus and there was some uncertainty whether he is on the ventilator or not. I do not agree with him on a political or moral plane, but I suddenly had a face to one of my numbers. More, I suddenly realised that according to the numbers I had been looking at, he has a 50% chance of dying if he ends up on a ventilator. I had this very strong thought that I desperately want him to survive.

I think this is a sober thought. It is easy to hide behind figures and numbers and lose their meaning. But the work on epidemics means that each figure or number has a meaning. And the meaning is of life or death.

On a positive note, there seems to be continuing evidence that Italy and Spain are slowing down, Austria and possibly Denmark and Czechia are thinking of relaxing the regulations, and even the UK and the US are not growing as fast as they were few days ago. Possibly, the actions are making a dent.

These are slightly different plots than last time, as they show new cases and deaths every day, but similarly, the start is at the left bottom corner and the end (meaning yesterday) is where the point is. If the line goes up, it means there are more and more cases every day. If the line is horizontal, it means the numbers can still be increasing, but slowly (by the same number every day). If the line goes down, we are still seeing new cases or deaths, but the everyday increase is getting smaller.

So a ‘peak’ (like a top of the hill) in this plot is not a real ‘peak’ in cases but is a good indication that we are on the right trajectory. The ‘top of the hill’ will come later but it is difficult to say how far away that is.

Note how long it took for China to lower the numbers. This possibly supports one of our scenarios in a recent The Conversation article on ‘Four graphs that show how the coronavirus pandemic could now unfold‘.

Cases are a better indication of what happens now; death records are delayed by a week or more but are more reliable.