Karl Friston and Anthony Costello: What we have learned from the second covid-19 surge?

And what does it means for the future?

By any metric, one should probably call it—the autumn surge has peaked. So what have we learned? Before the second peak, we made some bold claims—based upon dynamic causal modelling—that fatalities would peak “around 8 November.” [1-3] The timing was important because a peak at this time could not be explained by a second lockdown. In other words, the precautionary measures (i.e., tier systems) implemented prior to the second lockdown would have been more effective than generally assumed. [4] So what actually happened?

At the time of writing, deaths peaked at 481 per day on 9 November (based on the seven day average of positive tests by date of death). [5] One might argue that dynamic causal modelling was accurate to within days; however, this would be a bit disingenuous. The seven day average looks as if it will peak about 10 days later—at around 450 deaths per day. This peak rate is higher than we had predicted (by a factor of three); although less than the thousands suggested by forecasts of unmitigated outcomes from the Scientific Pandemic Influenza Group on Modelling (SPI-M). [6,7]

Predictive validity is not an issue for forecasts of unmitigated outcomes. However, it is an issue for dynamic causal modelling that tries to predict what will happen, including—crucially—our responses. Mitigations and interventions can be predicted because they are responses to the level of infection and its fluctuations (e.g., the reproduction ratio)—and can therefore be embedded into dynamic causal models. [8] The best way to underwrite predictive validity is to ensure the model has the greatest evidence, i.e., find the model that provides an accurate account of data in the simplest way possible—by comparing different models of the same data.

The second peak enabled us to “go back to the drawing board” and use Bayesian model comparison to ask what model components are necessary to explain the second peak more accurately. [9] In brief, to account for both the first and second peaks, it was necessary to equip the model with seasonal fluctuations and changes in mitigating responses (i.e., social distancing and lockdown). The latter installs a “memory” of exposure to the virus (quantified by seroprevalence). When the model was equipped with this “memory,” it accounted for the first and second surges more accurately; technically, the model had a greater model evidence. [10] Put simply, the evidence suggests we, as a population, appear to be responding more cautiously to the second peak, relative to the first—as evinced by the second lockdown and the comparatively smaller mortality rates. Furthermore, it suggests that the secondary wave as a result of relaxing restrictions on contact rates, as opposed to a second wave due to a loss of immunity. [11] Why is this important?

It is potentially important because it suggests the secondary and subsequent waves may unfold more slowly than the first. In fact, dynamic causal modelling predicts the next wave will be after summer, allowing for transient spikes due to Christmas and school holidays. [12] This differs from predictions prior to the second surge—and suggests a slow relaxation of mitigation responses (e.g., local tiers) over the next few months. Furthermore, it suggests that there will be an extended window of opportunity to drill down on test, trace, and supported isolation; especially with increasing coordination between central and local contact tracing teams. [13] However, a slower decline in the number of cases presents a challenge to contact tracing, which brings us to our last point.

One obvious question is what about vaccination? [14] Our provisional modelling suggests that an effective vaccine (under best-case assumptions) could defer a third peak until next winter. Crucially, if vaccination was combined with enhanced contact tracing and supported isolation, then community transmission may be suppressed. [15] In other words, the Christmas gift of vaccines may not, in itself, resolve things but put suppression within the grasp of well-resourced public health measures.

Under a pluralistic model of mitigations (i.e. restricted contact rates, an effective vaccination programme and supported isolation of contacts), predictions of transport use and workplace activity suggest we could return to summer levels in early spring and near normal levels by June, 2021. These predictions may be optimistic; however, there is one thing that we do know: the validity of predictions will increase as they inherit from experience.

Karl J. Friston, Scientific Director: Wellcome Centre for Human Neuroimaging. Professor, Queen Square Institute of Neurology, University College London. Honorary Consultant, The National Hospital for Neurology and Neurosurgery

Anthony Costello, UCL Institute for Global Health, University College London, Professor of Global Health and Sustainable Development.

Note: The quantitative predictions in this opinion piece are based upon dynamic causal modelling. Although this model has been optimised using Bayesian model comparison over the course of the pandemic, it is only one model. As such, any predictions or assertions should be qualified by the fact that they are entirely conditioned upon the model used, which may or may not be the best model.

Competing interests: Karl Friston and Anthony Costello are both members of Independent SAGE. They declare no other conflicts of interest or competing interests.


1] https://www.fil.ion.ucl.ac.uk/spm/covid-19/dashboard/local/
2] DCM uses variational Bayes to estimate the unknown parameters of models and then to assess the evidence for alternative models of the same data.
3] Modelling the pandemic—time is of the essence, The BMJ. https://blogs.bmj.com/bmj/2020/11/09/modelling-the-pandemic-time-is-of-the-essence/
4] https://www.gov.uk/government/speeches/prime-ministers-statement-to-the-house-of-commons-on-coronavirus-4-november-2020
5] https://coronavirus.data.gov.uk/
6] https://www.gov.uk/government/publications/coronavirus-cases-in-england-4-november-2020
7] https://www.gov.uk/government/groups/scientific-pandemic-influenza-subgroup-on-modelling
8] Adam Kucharski on Twitter: “Why do COVID-19 modelling groups typically produce ‘scenarios’ rather than long-term forecasts when exploring possible epidemic dynamics? A short thread… 1/” / Twitter
9] [2011.12400] Dynamic causal modelling of mitigated epidemiological outcomes (arxiv.org)
10] Bayesian model comparison allows one to evaluate the evidence for a new set of priors, relative to previous priors.
11] https://www.fil.ion.ucl.ac.uk/spm/covid-19/TR5_Second_Wave.pdf
12] We simulated a five-day relaxation of restrictions (by increasing the social distancing threshold by 50% from Christmas to New Year). A Christmas relaxation of this sort would cost an additional 2000 lives between Dec 24 and April 1 2021. Repeating the analysis with an effective vaccination program reduces this loss to just under a thousand (922).
13] Suggested steps for increased localisation of testing and tracing, 20 November 2020 | Local Government Association
14] UK authorises Pfizer/BioNTech COVID-19 vaccine – GOV.UK (www.gov.uk)
15] Defined operationally as the probability of self-isolating when infected but asymptomatic.