Clive Best

At the beginning of March Neil Fergusson modelled the impending Covid-19 epidemic for the UK  which was expected to begin in early April and consequently reach a peak in May, all based on the infection rate assumed at that time. His influential “Report9” circulated and published on March 16 reflected these underlying assumptions. The lockdown measures that he proposed  to suppress infections and thereby allow the NHS to cope with the predicted surge in demand for ICU beds were also timed for April. There seems to have been a widespread belief in SAGE at the time that the UK was 3 to 4 weeks behind Italy, so consequently we had ample time to plan measures accordingly. We can now see that this simply wasn’t true and infections were spreading fast in early March. This was mainly because of open borders to Europe and a lack of testing capability. Figure 1 compares the recorded deaths in Italy, France and England as of June 16.

Figure 1. Daily recorded deaths in Italy, France and in NHS hospitals in England. Note the overall similarity between  England to France. The criteria for recorded deaths vary between countries. Here  I am just using hospital deaths registered by  day of death for England (population: 56 million)

In Figure 1.  I am plotting just the hospital deaths in England as recorded by the NHS because this probably best represents the dynamics of community wide infections. (The tragic deaths that have also occurred in care homes are another story!). Note how the epidemic begins simultaneously in England and France, both of which lag about 2 weeks behind Italy.  However by the end of April  all 3 countries then tail off together at almost the same rate ending together.  The Italian epidemic just seems to have lasted longer.

Ferguson originally released his code for “CovidSim” on GitHUB in May, together with the parameters files that describe the UK, updated to describe the emerging epidemic data. The unmitigated run he used on GitHUB show that he increased Ro to 3 because it was discovered that early UK infections were doubling every 3-4 days. His suppression  simulation was really based on the consequent  March 16 Household Quarantine (HQ) and limited Social Distancing (SD) measures as announced by Boris Johnson, then followed 7 days later on March 23rd by stringent Place Closures(PC). On March 23rd Boris Johnson announced that all pubs, restaurants,  shops, schools, Universities would close forthwith and that everyone should stay at home as far as possible.  March 23rd is therefore considered to be the real lockdown date for the UK, forgetting that a week earlier social distancing had already been already been introduced. As a result of all this the parameter file that Fergusson uses to simulate what really would happen during the UK epidemic is called PC7_CI_HQ_SD, where “PC7” symbolises the 7 day delay between March 19 and March 23 in implementing full lockdown.

Firstly we look at the unmitigated predictions. Figure 2 shows the  comparison between the original Report9 Neil Fergusson model predictions as made in early March with those from his updated May version.

Figure 2. A direct comparison between Fergusson’s Report 9 simulation with R0=2.4 and the later UK simulation in May following the start of the outbreak.

The most striking feature here is the nearly one month anticipation of the real infection peak compared to the earlier Report9 simulations. Note also in passing that the original Report9  runs were made just for Great Britain and for some reason excluded Northern Ireland. This however can only explain a small proportion of the increase in  infections. The major reason for this increase was essentially due to using the observed increase in R0 to 3.0. SAGE were estimating that infections were doubling every 3 days.

Secondly we can compare the new May CovidSim “lockdown” simulations of deaths against the actual statistical data as recorded up to June 16th (Figure 3). I am using COVID-19 deaths as a measure of infection rates mainly  because these are the only consistent numbers across time.

Figure 3. A comparison between the Ferguson model simulation of the UK lockdown with the actual death data vas recorded across the UK including Care Homes. The total unmitigated deaths reach 620,000. The recorded cumulative UK deaths were 41736 on 16 June.

The new model is clearly predicting more deaths than were actually recorded even if we now also include care home deaths.  These care home deaths were more a consequence of NHS lockdown measures rather than community infections as simulated by Fergusson. So what does all this mean ?

Ferguson had assumed an IFR (Infection Fatality Rate) of 0.9% and as a consequence his model predicted that 70,000 deaths would occur by June 16. In reality 41736 total deaths have occurred across all settings by then. It is likely that he calculated the infection rate correctly but simply used a too high value for IFR.

Therefore I would  conclude that IFR is  ~0.5%, and probably less than that once you exclude hot spots of infections such as those occurring  inside care homes.

On March 16 Boris Johnson held his daily COVID briefing and for the first time introducing tentative social distancing measures. That same day Neil Ferguson had formally  published his simulation of how the UK epidemic would unfold and which suppression measures were needed – Household Quarantine, Place Closure, Case Isolation and Social Distancing (Report 9).  The paper must have been circulated within SAGE far earlier than that.  A full lockdown was finally introduced a week later on March 23. Unfortunately Fergusson’s  timing was about a  month out of date and the real situation was far worse than even he assumed. The real number of cases and rate of infection by March 16 in the UK was in reality far higher. However  no-one knew this at the time because there was no community wide testing amid what now appears to be an air of complacency by PHE.

We can now look back and compare what actually occurred with the original Report 9 simulations which I have rerun. This is shown in Figure 1.

Figure 1. Neil Ferguson’s COVID simulation results (Report 9) as compared to actual COVID deaths as recorded in English Hospitals. The peak in English deaths occurred on April 10. This is compared to the Report9 green lockdown simulations and  a one month delay (solid black) of the model.

The peak in infections and deaths occurred one month earlier than he or anyone else had anticipated. Fergusson had predicted in report 9 that the peak would occur much later  around mid May. That was probably because he was using the Chinese data for R0 (2.4) and used an optimistic estimate of  the number of current UK infections. When the report was published there had been very few confirmed deaths.  However we now know there were probably  tens of thousands of infections. SAGE  now estimate that R0 in early March was 3 and that the number of infections was doubling every 3 days.

If the UK had locked down a week earlier the resultant number of deaths would have been much lower with at least 20,000 fewer deaths and we would be exiting lockdown by now (June 7). However at the time no-one knew the full extent of infection due to the total lack of community testing.

On March 16th Neil Ferguson’s team published “Report 9” which changed government policy and triggered a “lockdown” a week later. The results of his simulation showed that the number of COVID  patients would soon overwhelm the ~4000 ICU bed capacity in the NHS. The code that produced his results has now been made available and I have spent the last few days struggling to get it working. Here are the first results I get after running Ferguson’s “Report 9″model.

COVID simulation for UK if left “unmitigated”

and in yet more detail.

Predicted “unmitigated” deaths using R0=2.4 IFR = 0.9% as used in report 9.

I was surprised to see the date of the peak predicted by the model because in reality the epidemic  occurred about a month earlier (starting March 1). So it looks like Ferguson originally thought that we had much more time to prepare for this emergency than in reality we did have.

The main impact of this report were the  measures he proposed to suppress the epidemic thereby avoiding “overwhelming the NHS” and “save lives”. I have spent the last 3 days struggling to get his code working and it has been a bit of a nightmare. The released procedure as was published on GITHUB could only really be run on a supercomputer,  while instead I have an iMac! There are 4 types of suppression interventions.

1. PC – School and University closures, restaurants, bars, non-essential shops etc.
2. CI – case isolation (7 days)
3. HQ – Household quarantine (14 days)
4. SD – Social distancing (at various levels)

The newly released “report9” process proposes to run the Covid-Sim model 10 times (multi-threaded) and then take the average. (The main reason to run it 10 times is because you get slightly different values each time).  In addition to this there are an additional 45 combinations of intervention strength and 4 different values of R0  (2.0, 2.2, 2.4, 2.6 ) to run. This makes a grand total of 180  CovidSim batch jobs, which is equivalent to 1800 single threaded runs! This can only really be run on a supercomputer. The full suite of combinations is basically impossible to run on my iMAC. So instead I decided  to restrict all my combinations to a single run (instead of 10) and to use only R0=2.4 because this was used in his original paper.  This produces a more reasonable set of 60 sequential runs which still took me about 2 days to finally finish while getting a headache. Here are the results I get for one  typical 4 level intervention scenario, more or less  corresponding to those shown in report 9.

Impact of 4 suppression scenarios on predicted deaths. The green curve more or less represents the lockdown measures the UK consequently adopted. Note that the dates are  a month later than what actually occurred. The maximum peak in deaths/day reached in the green scenario is ~ 400

Intervention detail. I am not yet quite sure why the second peaks appear yet !

The full lockdown measure finally adopted is shown in green resulting in a smaller peak in deaths after about 28 days followed by a long tail. So how do these prediction compare to what actually happened in reality. UK lockdown measures were introduced on March 23rd a month earlier than envisaged above. Here are the daily deaths in hospitals (excluding care homes) as reported by the NHS.

UK Hospital deaths by actual date

This indeed shows the same shape but twice as many deaths occurred than expected, yet at no time were ICU beds overwhelmed. The outbreak occurred a month earlier than Ferguson predicted. This  seems to be because there were far more infections in the community than were originally thought. It is now estimated that R0 was actually 3 instead of 2.4.

Hindsight is a wonderful thing, but it seems pretty clear that the UK  should probably have locked down a week earlier, and as a result total deaths probably would have been halved.