Has England reached herd immunity level – part 2

An update on the previous post on the UCL model and herd immunity levels. I just thought of adding a couple of further thoughts on this topic.

Firstly, there appears to be growing evidence of a potential for new strains (Brazil, South African, Indian) to overcome the immunity created by the previous infections.

The rapid growth of cases in Brazil and now in India suggests that either our estimates of Herd Immunity Threshold (HIT) are too low, or people who have SARS-CoV-2 antibodies can still be infected.

Secondly, there is an interesting interplay of heterogeneity and HIT. Heterogeneity, be it in the infectivity or susceptibility, is normally thought to lower the HIT. This basically is caused by the infection “burning” through the most susceptible parts of the population first.

As a result, we end up with a population where those who are not yet immune are protected by their lower susceptibility. This results in a lower value of HIT than predicted by the homogenous theory.

However, there is another trend that counteracts this process, and the one which seems more dominant at this moment. We now have a very uneven distribution of immunity due to vaccination.

Those who are potentially most likely to become infected (those in the BAME population, in deprived areas, or those who are vaccine-hesitant or anti-vaccine) also have the lowest vaccination coverage.

Thus, even if on average we can reach the HIT, these pockets of low-immunity, high-susceptibility/high-infectiousness, will keep the infection going and possibly creating the conditions where new strains can arise.

Even more arguments for the #ZeroCovid strategy… Let’s just keep going for a while longer, paying particular attention to those who are most at risk, to reduce the overall levels of infection until we can bring the vaccination higher.

Is England reaching herd immunity level today?

Much in the news has recently been made of a statement by a group of modellers led by the University College London that England will be reaching the herd immunity threshold (HIT) on April 9th, 2021:

A herd immunity threshold (of 73.4%) will be reached this week on 9 April 2021.


The popular view is that once we reach the HIT, the reproductive number will always be smaller than 1 regardless of what we do, the number of cases will always decline and hence the pandemic is essentially over. Unfortunately, none of this is in fact correct – but the problem is less with the UCL model and more with our – scientists – ability to communicate uncertainty, and our – the “Joe public” – ability to understand it.

Let’s start with the model. There are currently several models of the coronavirus pandemic in the UK, including the three “official” ones, by Warwick, LSHTM and Imperial groups. In addition, there are many other models by different groups, with different level of complication and addressing different questions. All of these models attempt to capture the key elements of the transmission – contact structure, probability of infection, age-dependent susceptibility and fatality rate, loss of immunity.

They also attempt to factor in the uncertainties associated with our lack of knowledge of some pretty important elements. Primarily, this is related to the actual number of those who are immune to the infection. The models are essentially used to “reconstruct” this number, and different assumptions can lead to different numbers.


Why is it important? Our best understanding of how coronavirus spreads suggests that once the proportion of those who are immune reaches a certain threshold, the infection numbers will stop increasing. The epidemic will not be over, there will still be people becoming ill and dying, but the overall trend will be downwards.

The “Holy Grail” of epidemic modelling is the knowledge of what this level is and countless arguments have been presented for different numbers. To some extent, however, this is a bit of a “red herring”. This number depends on how fast the disease is spreading, but this, in turn, depends on how we behave and what we do to control the spread.

There is, however, an upper limit to this threshold value, corresponding to the situation with no lockdown, mask use, hand washing, or staying at home (international travel is a slightly different thing). Good evidence suggests a value of 60-80%. It could be somewhat higher – as the “new variants” have higher potential for spread, or it could be lower – if there are substantial levels of variability in how susceptible people are or how they make contact. Somewhere in the middle, there is 75%, so we might stick to this number.

So, the models predict that once the proportion of immune people – which is unknown but estimated by the model – reaches 75%, the trend in the disease levels can only be down. But, what are these model estimates? How far are we from the “magic” threshold?

In principle, trying to estimate this value is a hopeless case, because of a combination of asymptomatic spread and low testing coverage and efficiency. Thus, at the beginning of the epidemic, we only tested – and reported – those with symptoms or even just those who came to a hospital. Anybody who did not have severe symptoms never made it as a number.

It is a bit like in the parable of the blind sages and the elephant.

By Ohara Donshu, Japanese, died 1857 – Online Collection of Brooklyn Museum; Photo: Brooklyn Museum, 1993.57_IMLS_SL2.jpg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=10967373

It is a story of a group of blind men who try to guess what the elephant is like by touching it and only experiencing a small part of it. In the same way, we are trying to guess how many people have already been infected and hence might be immune, based on the case notifications.

Different models might make different assumptions and so get different estimates. The graph below shows such estimates from four models, compared with the actual data which represent the recorded cases. As we can see, the elephant we managed to recreate has some “elephant-like” features (the first peak, followed by a summer break, and the double winter peak), but the estimated number of “true infections” and hence the number of those who might be immune by now differs massively.

The situation is actually not as hopeless as it sounds. We can actually test people for the presence of antibodies and then verify that our models are correct – and reject or modify those that are not. By the way, antibodies are molecules that a body produces in response to infection (or vaccination) and their presence suggests some levels of immunity.

A month ago, in a survey, 54% of people in England tested positive suggesting that as many as that had contact with the virus. With relentless vaccination since then, I would not be surprised we might soon reach 75% testing positive or vaccinated with one dose. The numbers of those with two doses (myself included) are also going up.

But this almost certainly does not mean 75% are fully immune. The vaccine is not perfect (and the 85.2% efficacy assumed by UCL might be an overestimate). The presence of antibodies does not mean the person is completely safe. We still do not know how much vaccination stops transmission; if it does not fully, the HIT will be higher than the 75% quoted above.

As even small changes in these percentages can cause large changes in the way the virus spreads, there is a huge uncertainty associated with the size of the “third” wave. In the light of this, I think the UCL group are certainly unwise to make statements about reaching the HIT on a particular day.

Finally, does this mean the pandemic is over in the UK after today and we can relax all social distancing measures and stop vaccinating? Unfortunately, no. We do not know how well prior exposure to the virus guarantees immunity to the new strains. We know the new strains lower the efficacy of the vaccine. We know the immunity wanes in time. Our models are probably good enough, but not perfect to predict that the exact value would be reached on a particular day.

But even more importantly, the HIT only means that the daily count of infections will be going down once we reach that level. But there will still be many new infections and many deaths. More, models tell us that if we relax all regulations now, the speed with which the virus will decline will be much slower – which means many more sufferings and deaths. As throughout the last year, the more intensively we fight the virus, the quicker it would go away. Let’s keep doing this.

It has been pointed out to me that my second vaccination dose is not counting towards the English herd immunity levels, but the Scottish ones.

Worse than flu?

From time to time, I hear an argument that the COVID-19 pandemic is actually not as bad as the politicians and scientists try to argue. One argument goes along the lines that the mortality in 2020/21 is actually similar to what happens in other years from seasonal flu, other diseases, or other causes like car accidents.

Many news outlets produce daily reports on COVID-19 death numbers. These data, while very useful for monitoring the current state of the outbreak, need to be properly interpreted. Firstly, they usually represent ‘death by reporting date’, i.e. how many deaths are reported by authorities on that day. There are of course delays with reporting and so the current value might be significantly lower than the actual number (Sweden is notorious for long delays of death reporting). Of course, the numbers will eventually catch up but might create a (temporary) impression that the pandemic is dying out.

Secondly, the reports concentrate on deaths labelled as COVID-related. There are again problems with the process of assigning deaths to COVID and different countries use different (and changing) criteria. The procedure is often criticised for attributing to COVID deaths that are caused by other diseases.

The ‘excess death’ record is a measure that is not that easy to question, as it looks at death records, without any attribution to COVID. In this approach, we compare the total number of deaths in 2020/21 season to values in previous years. I used the deaths records in one of my early posts on COVID, back in April 2019. We now have much more data to look at and I am going to make use of them here.

Deaths in the US since 2015. Different coloured lines show years 2015-19 (black is 2015, light blue is 2018 and pink is 2019) and red shows years 2020 and 2021. The horizontal line shows the maximum pre-2015 value.

In the graphs above, weekly US death notifications are shown for 2020 and 2021, with different coloured lines showing values from individual years 2015-21.

Looking first at the general trends before 2020, roughly 54,000 people die each week in the population of about 330 million; 2.8 million deaths a year from all causes, or about 0.85% of the population. The numbers vary over the year and typically are higher in winter and lower in summer. Some years, particularly when the seasonal flu is bad, have higher mortality in winter months, November to February. In the period 2015-2019, the highest point was in the second week of January 2018, with 67,661 deaths that week. Finally, the overall number of deaths increases slightly over years, reflecting mainly the increase in the population, but also the declining general health.

Compared to this, the highest level of deaths in 2020/21 was in the last week of 2020, with 82,255 deaths recorded. There were two periods when the weekly number of deaths exceeded even the highest value observed in winter 2018: Spring 2020 and Winter 2020-2021. Summer 2020, when in other years the deaths are much lower, got nearly to the same level.

Even more striking are the total yearly numbers for the period of March of one year to February next (to compare with 2020-21). In the ‘bad flu’ year 2017-2018, 2,839,711 deaths were recorded. In the last year before COVID, 2019-20, the number was 2,860,458.

In the COVID year, 3,447,015 died, an excess of 586,557 people, of about 20% of “typical” death numbers.

Now, these are all deaths, so include not only those who died of COVID, but also those who died because of COVID. People who did not have COVID but died because of lack of medical access are included, and those who died because of economic hardship.

It will take, I am sure, a long and detailed study to disentangle the different causes of COVID-related and unrelated deaths, but it suffices here to note that the highest excess deaths have occurred not in periods of the strictest lockdown measures (as reflected in the Google mobility data below) but when there was the highest number of reported COVID cases. This makes the case that the majority of deaths are not COVID-related outrageous.

US mobility data from Google. The graph shows the reduction to the baseline at the beginning of the COVID outbreak.

In summary, COVID-19 is not like flu but – for the US and for many countries in the world – a disaster that is causing immeasurable suffering and deaths.