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expert reaction to non-peer reviewed modelling presented on a dashboard suggesting that ‘a herd immunity threshold (of 73.4%) will be reached this week on 9 April 2021’

The prediction, based on modelling at University College London (UCL), was reported on by the Telegraph this morning.


Prof Paul Hunter, Professor in Medicine, The Norwich School of Medicine, University of East Anglia, said:

“I am quite sceptical of the conclusions reported by the Dynamic Causal Modelling group at UCL that we will reach herd immunity on 9th April. For any infection herd immunity can only be said to have been achieved if a sufficient proportion of the population have acquired immunity either from immunization or natural infection to bring the R value below 1 that the disease with ultimately disappear. But for herd immunity to really happen that immunity has to last. At present we do not know how long the immunity generated by immunization will last nor what impact the emergence and spread of new variants will have on vaccine effectiveness.

“Our own analyses in a pre-print published in January was one of the first to show that herd immunity is unlikely to be achieved with current vaccines and the Warwick group and now Imperial have all released pre-prints or presented papers to SAGE that effectively come to the same conclusions.

“Whilst it is not totally clear from the UCL website how the assumptions used in their model were arrived at. But there are a number of issues that worry me.

“The real time estimate of R used is 1.12 (credible interval from .77 to 1.46) on 4th April which is somewhat higher than was estimated to be the case by SAGE at the time. The authors then say that they expect the R number to fall over coming weeks. It may indeed fall but the R number at present is the effective R value during a time when we are in lockdown. As lockdown eases R will most likely rise and this is the reason why most modellers and epidemiologists consider a further wave of inflection almost inevitable. Herd immunity during lockdown does not equate to herd immunity in reality and we really have to be careful not to muddle these two together. Otherwise we will mislead the public and potentially undermine a lot of the hard work of the past few months.  

“As far as I can tell no account has been made for the possible/likely spread of the new variants with escape mutations such as the South African and Brazilian and indeed the daughters of our own Kent variant that have acquired the E484K escape mutation. These variants are present in the UK albeit still at low levels but are likely to increase as lockdown eases.

“Also as far as I can tell the authors have made no account of asymptomatic transmission and the even lower effectiveness of current vaccines at preventing infection compared to mild and severe infection.

“In their report the authors state “Much like long-term weather forecasts, the ensuing predictions should not be taken too seriously because there is an inherent (although quantified) uncertainty about underlying epidemiological and socio-behavioural variables”. I think they are right in saying this.”


Dr Louise Dyson, Associate Professor in Epidemiology, University of Warwick, said:

“This research does not appear to be internally consistent. Friston asserts both that R=1.12 on 4th April and that we reach herd immunity on 9th April, even though his estimate for R on 9th April still looks to be above 1. He defines the herd immunity threshold based on what would happen if we returned to pre-pandemic contact rates. So the assertion is that cases were rising on 4th April (under lockdown conditions) but if we released lockdown and went back to pre-pandemic contact rates on 9th April then that would keep R below 1 and cases would decrease. This is not consistent.

“Friston’s historical estimated herd immunity threshold changes with each new model fit. The previous fit from 27th March 2021 reached a minimum of roughly 50% for last August, while the new fit is 40% for last August, and these minima are mirrored for this year. It would seem unwise to base any policy decisions on estimates that change so much in their understanding of the history of the epidemic, without investigating the reasons for such changes.

“In addition, the forecasting model also predicts governmental unlocking and/or the population response to it, and in these predictions expected “a further easing of restrictions on 7 April 2021″. This is despite the published government roadmap which does not allow for further easing before 12th April.”


Prof Rowland Kao, the Sir Timothy O’Shea Professor of Veterinary Epidemiology and Data Science, University of Edinburgh, said:

“An important consideration that any model attempting to predict levels of immune protection resulting in herd immunity (i.e. sufficient number of protected individuals that the R number is below one in the absence of restrictions), is the role of spatial variation in those levels of immune protection, as there is evidence that the circulation of COVID-19 largely occurs over short geographical distances, resulting in clusters of infections (see for example, here Thus it matters very much for example, whether two different areas with the same population have attained 80% protection, or an overall average of 80% but where one area is (in extremis) 100% protected, but the other area only 60%, as there is much stronger risks of infection circulating in the less well protected group. A further consider is the potential role of superspreading events, where levels of immune protection would have to be extremely high, in order to prevent an outbreak.  Therefore we have to consider a number of factors. First, the underlying number of people who have already been infected will vary considerably from region to region – as an extreme example, the Scottish Highlands and Islands have had very low infection levels so very little naturally induced immunity in those populations. Second, there is evidence that while the level of protection due to natural immunity is relatively high after six months for the under 65s, it is considerably lower (on the order of 50%) for the over 65s (see The over 65s are thankfully relatively well covered by vaccination now, unfortunately, there is also evidence that the uptake of vaccination has been highly variable, with in particular some ethnic groups and people in deprived communities substantially less likely to have been vaccinated (see for example here: These are also the groups where individuals more likely to be seriously affected by COVID-10 infection. Thus any assessment of when we are likely to attain herd immunity which does not consider these heterogeneities, would be overly optimistic in its predictions of our levels of protection.”


Prof Christl Donnelly, Professor of Applied Statistics, University of Oxford & Professor of Statistical Epidemiology, Imperial College London, said:

“This morning (8 April 2021), we published a report on the 10th round of the REACT-1 survey.  This survey measures swab-positivity for the SARS-CoV-2 virus in the community in England.  The first significant relaxation of the third national lockdown happened on 8 March.  Round 10 swabs were collected from 11 to 30 March.  During Round 10 we estimated an R number of 1.00 (with a 95% confidence interval from 0.81 to 1.21).  This indicates that with all of the immunity in the population at that point (both vaccine-induced and naturally acquired), the social distancing restrictions in place in March were just enough to keep infections from increasing and not enough to make them decrease (with the level of uncertainty in this estimation indicated by the confidence interval).  If the population of England were to reach the herd immunity threshold, then it would mean that without social restrictions the immunity level would be sufficient to keep infection rates from increasing and as immunity increased further, infection rates would go down.  Given how limited our social contacts have been throughout March, the REACT-1 results are strong evidence that herd immunity is not imminent.  This is a conclusion that can be drawn directly from the R estimate obtained from the 10th round of REACT. It does not require any assumptions to be made about population immunity other than that it will not have changed dramatically between mid/late March and early April.”


Dr Adam Kucharski, Associate Professor in Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, said:

“I made these comments on a previous iteration of this modelling but my concerns still apply.

“Unfortunately, the modelling approach used to produce this analysis has a history of making over-confident and over-optimistic predictions. In early September, a pre-print claimed that, ‘The best model of UK data predicts a second surge of fatalities will be much less than the first peak (31 vs. 998 deaths per day, 95% CI: 24-37) – substantially less than conventional model predictions.’ In late September, the lead author claimed, ‘When one models what is likely to happen – in terms of viral spread and our responses to it – a plausible worst-case scenario is a peak in daily deaths in the tens (e.g. 50 to 60) not hundreds, in November. This may sound rather precise; however, this kind of modelling has already proved to have predictive validity to within days.’

“There is currently a lot of uncertainty about vaccine effectiveness on reducing transmission, the duration of vaccine protection, characteristics of new variants, and the future control measures countries may keep in place or relax. However, it is not clear from the online model description how it incorporates these uncertainties, or what has been updated since it made its predictions above. Models can be a useful tool for exploring potential dynamics under different assumptions about transmission and control measures, but it’s crucial that these assumptions are made clear, and known biases in past model performance are addressed before new results are publicised.”



All our previous output on this subject can be seen at this weblink:



Declared interests

Prof Christl Donnelly: “I have funding support from the MRC and NIHR.  I am a co-author of the REACT surveys.”

None others received.

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