Oliver Johnson

Has South Wales reached herd immunity?

Has South Wales reached herd immunity?
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Few topics during the Covid pandemic have caused more controversy than the Herd Immunity Threshold, the level of immunity at which the virus can no longer spread through a population even once social distancing is relaxed. Confident past predictions that Sweden or India had reached this have been swept away by sizeable second waves, and certainly we cannot tell from graphs of falling cases alone that herd immunity has been achieved.

However, considering the latest data, I believe it is worth asking whether parts of the UK have passed the Herd Immunity Threshold. The answer may be 'not quite yet', but it can be useful to think why. Essentially, herd immunity should be possible given enough infections and vaccinations, conditions that may apply in parts of South Wales, for example. But are numbers there sufficiently large, and how would we tell?

In conventional epidemic models, the Herd Immunity Threshold can be found using the famous R number. Remember that we write R0 for the average number of people that each infected person themselves infects, at the start of the pandemic.

For example, R0 for the so-called Kent variant might be around 4.5. If 78 per cent of the population were immune, the average number of infections passed on would only be 22 per cent of 4.5, or just less than one, meaning the epidemic would eventually die out by this herd immunity effect alone. For a variant which was 50 per cent more transmissible than the Kent variant, we would need just over 85 per cent of the population to be immune

Some authors argue this 78 per cent figure is too high. Perhaps there is pre-existing immunity in the population? Perhaps 'super-spreaders' with many contacts are infected first, and by becoming immune give a disproportionate reduction in infections? However, in my view predictions arising from such models have too often proved overly optimistic, and the standard calculation still seems broadly accurate.

It is worth remarking too that this calculation describes the situation 'on average'. Infection is a random process, and having achieved herd immunity is somewhat like gambling in a casino with the odds skewed in your favour. Reaching the Herd Immunity Threshold certainly does not mean nobody else can become infected, nor can it be taken as a license for riskier behaviour.

Indeed, further outbreaks would be entirely possible, particularly in unvaccinated communities such as schools. However, ultimately, such outbreaks should be limited by the difficulty of them spreading into a significant proportion of the wider population, and they should be less likely to start with fewer cases outside.

A further caveat is that seasonal effects in both human and virus behaviour may cause the Herd Immunity Threshold to vary. Indeed, immunity will not last forever, meaning we can return below a Herd Immunity Threshold even once it has been achieved.

Nonetheless, Israel led the way on vaccinations and now appears close to some form of normal life, with very low case and death numbers, despite being close to usual levels of mobility. While they may not be technically at herd immunity, it certainly looks like it. It is natural to ask if the UK is close to achieving the same, and whether herd immunity might already exist in some areas.

To understand this, we need to estimate immunity due to both infection and vaccination. There is uncertainty regarding these numbers, but in certain areas they are clearly both very high: for example, look at South Wales.

Consider Merthyr Tydfil, which was hit particularly hard by the second wave of the virus. It has had the UK’s fourth highest number of positive tests per head, at over 11 per cent of its population. The number of people who will have had Covid will be higher (due to the large number of asymptomatic cases, early unavailability of tests and other factors). 

The figures show Covid deaths account for 0.35 per cent of the population. If we assume the virus kills one per cent of those it infects, then there should be 99 survivors for every fatality (this is a conservative estimate) so 35 per cent will have been infected.

Of course, 35 per cent infections is not enough to achieve herd immunity. But we can now add to that vaccinations.   

Roughly 60 per cent of the Welsh population have received a first dose, and 25 per cent are fully vaccinated. Amongst adults, the figures are 76 per cent and 33 per cent respectively. Although vaccinations are not perfect, we might estimate that 50 per cent of the Welsh population would be immune due to vaccination.

Clearly, we cannot simply add 50 per cent and 35 per cent together to estimate total levels of immunity – some people will have been both infected and injected. However, a simple argument is to imagine that both processes take place at random, making the proportion of people with neither form of immunity be 50 per cent of the 65 per cent non-infected population, or 32.5 per cent.

If current levels of immunity in Merthyr Tydfil are indeed as high as 67.5 per cent, this isn’t 78 per cent, but it’s not so far away. It may even be comparable to Israel’s immunity level, where around 60 per cent of the population are fully vaccinated, but only 0.07 per cent of the population has died.

The effects seen already are certainly striking: Wales currently averages under ten cases per 100,000 people per week. Merthyr itself has seen only six cases in the last week, down from 751 in the peak week in December. Similar figures can be observed in nearby boroughs such as Blaenau Gwent and Rhondda Cynon Taf, which also endured very high death rates.

In that sense, the somewhat binary question of herd immunity may be moot. It certainly seems plausible to me that immunity levels are high enough that with a minimal level of voluntary measures and an ongoing test-and-trace programme, life could be close to normal with very low risk, unless we encounter a more transmissible variant.

As vaccinations continue, immunity in Wales will rise further, and such calculations will move in our favour in more of the UK, with parts of Lancashire and Merseyside also worth monitoring. It’s worth noting that countries with lower levels of infections will need a more extensive vaccination programme to achieve the same effect without risking a sizeable exit wave on reopening.

In that sense, this analysis can give cautious optimism about the current UK position, and our prospects for unlocking.

Written byOliver Johnson

Oliver Johnson is a professor of information theory and the director of the Institute for Statistical Science at the University of Bristol.

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