Karl J Friston, Anthony Costello , Deenan Pillay https://www.medrxiv.org/content/10.1101/2020.09.01.20185876v1
3rd September 2020
Draft comment by – T Andrew Broadbent CES Economic & Social Research info@ces.org.uk
Overview
This important paper claims to transcend the large number of ‘conventional’ epidemiological ‘SEIR’ models (Susceptible, Exposed, Infectious, or Recovered) of the current pandemic. Its fascination lies in its attempt to ‘compare SEIR models of immune status’ and derive results more directly from the data available.
It uses ‘Bayesian inference’ on data from 10 countries from 25 Jan to 20 June 2020 to estimate the daily proportion of people in each country who are (i) not exposed to infection(ii) not susceptible even though exposed (iii) not infectious even when susceptible. These sub-populations are what the authors call ‘dark matter’. It concludes that many more of the population are ‘effectively immune’ than generally understood, and so the second wave can be indefinitely postponed or suppressed without successive lockdowns as concluded from some of the conventional models.
The immediate issues and queries seem to be :
- Suppression is said to depend on an effective Track and trace system, as with some ‘conventional’ models. The practical policy implications are thus not very different from studies which suggest maintaining restrictions until infection is very low, so as to enable managing with track and trace, without needing to reimpose universal lockdown.
- The proportion of the population isolating/shielding dominates the results (eg Germany) . This is social behaviour and government policy, not ‘dark matter’ in the way susceptibility and infectibility may be, being more biologically determined.
- The parameters in the model are estimated within limits determined from external sources This may include the predominant ‘effective population’ parameter – the population who are not shielding.
- ‘Effective herd immunity’ is a somewhat troubling term – given overtones of ‘let the old die’ in some policy discussions of ‘herd immunity’.
- It claims to incorporate all the different data collection biases in different countries, such as testing people with or without infection. Would it be worth including countries with early success in suppressing infection – Taiwan, S Korea, China, New Zealand etc?
‘Effective’ herd immunity?
It references other studies which also look at ‘heterogeneity’ of the population, where the first wave either kills or makes immune the more susceptible population – so that a second wave necessarily involves a less susceptible population and will tend to be lower than the first wave, other things being equal.
It concludes that ‘effective herd immunity’ following the first wave of infection is much higher than suggested by the proportion of people who have been infected and recovered and may now be immune – ‘seroprevalence’ . This is now in the range 5-7% in the UK.
The term ‘herd immunity’ prompts wariness following the UK government’s early discussions which were interpreted as contemplating 60-80% of the population becoming infected with 500K-1 million deaths. ‘Culling the old and infirm’ was one interpretation. The paper concludes that having less than 20% of the population infected and recovered could be enough to dampen a second wave.
The second wave – a ten-fold reduction in infection and death?
A main claim of the paper is that the second wave could be postponed indefinitely, or if not, have a factor of 10 fewer infections and deaths than predicted by some SEIR models, (deaths peaking at 30-100 per day in the UK, compared with 1000 per day at the peak of the first wave) .
But this projection, has in common with the conventional models, a heavy reliance on an effective FTTIS (‘Find, Test, Trace, Isolate, Support’) system in order to isolate those infected or exposed to infection. But the paper suggests that only 25% efficacy of FTTIS is needed, compared to the present official target of 80%.(?)
Dark matter – very high?
‘Dark matter’ seems a very high proportion of the population. From one illustration (figure 2) dark matter results in under 20% of the population being infected. Almost 50% of the total population are not exposed (shielding/sequestered), so that only half the populations is ‘effective’ in the epidemic. Of those who are, 50% are not susceptible, and of those who are susceptible 50% are not infectious.
The proportion of the total population which is non exposed (self isolating, shielding, sequestered) would seem to be very dependent on people’s behaviour and on government instructions, and thus on the social context and time lapse of the pandemic. The other components of ‘dark matter ‘ – susceptibility and infectibility – seem more biologically determined, not so subject to behaviour and social and policy context.
Data – why not include countries with greater success in suppressing the first wave?
Although the FTTIS is said to be enough to limit or suppress the second wave without a ‘lockdown’, the Bayesian inference was conducted on countries, many of whom who were in some kind of lockdown for at least part of the period. They are the 10 countries with high death rates.
The data is from USA, UK, Canada, Spain, France, Italy, Belgium, Germany, Mexico, and Brazil . It would have been interesting to include countries which largely succeeded suppressing the virus in the first wave, with either very short sharp lockdowns, or early interventions of intense FTTIS, namely Taiwan, South Korea, China, Hong Kong, Singapore, New Zealand.
Many model parameters are influenced from outside the model. (?)
There ar 25 parameters listed in the model, and their levels and potential variation – are apparently influenced by external empirical studies outside the model, and are listed as ‘priors’. This apparently influences the final estimated parameters after the model has been run. (?)
Parameters include the effective population, the probability of going out, social distancing threshold, critical care capacity threshold (per capita), Infection, proportion of non-infectious cases, effective number of contacts, effective number of contacts: work, transmission strength, infected period , infectious period , proportion of non infectious people etc. etc.
Rich findings – country by country results – ‘effective population’ dominates?
The paper suggests that only Spain, and Brazil don’t exhibit the heterogeneity embodied in the model – in that their whole population seems to participate in the epidemic – their ‘effective population’ is equal to the whole population, with almost no one isolating, or shielding.
The country comparisons involve changing the input parameters, so as to eliminate each component of heterogeneity in turn. The parameters – effective population, non susceptibility, social distancing threshold, decreasing seropositivy are each removed in turn.
Germany and Canada have by far the smallest proportion of ‘effective population’ due to their high levels of shielding – this seems to determines their relatively good performance and low level of deaths, – it would be useful to learn more about how far this parameter is set ‘prior’ to the model.
There is much less variation in the proportion of the effective population susceptible to infection – from ~67% in Spain (operating on an effective population almost equal to the whole population) , to ~47% in Canada.
Similarly there is low variation in the proportion of susceptible people who are non infectious – from ~60% in Canada and Italy and to ~45% in Germany, France , and USA .
Some more details
The claim is that the analysis can incorporate all kinds of real world fuzziness in the data – by modelling latent variables such as the bias towards testing people with or without infection or, the time-dependent capacity for testing. ‘Everything that matters —in terms of the latent (hidden) causes of the data—can be installed in the model, including lockdown, self-isolation and other processes that underwrite viral transmission’.
This is a ‘LIST’ model with four factors (Location, Infection, Symptoms and Testing). It models the probability of people being in different states, and produces two outputs – positive cases, and deaths .
The states in each factor are::
Location – Home, Work , Hospital, Isolated, Removed
Infection – Susceptible, Infected, Infectious, Sero negative, Seropositive
Symptoms – Health, Symptoms, Severe, Deceased
Testing – Untested, Waiting, Negative, Positive
Each individual in the population has to be in one state, and only one state, within each of the four factors.