Change of reporting basis
The UK Government yesterday changed the reporting basis for Coronavirus numbers, retrospectively (since 6th March 2020) adding in deaths in the Care Home and and other settings, and also modifying the “Active Cases” to match, and so I have adjusted my model to match.
This historic information is more easily found on the Worldometer site; apart from current day numbers, it is harder to find the tabular data on the UK.gov site, and I guess Worldometers have a reliable web services feed from most national reporting web pages.
The increase in daily and cumulative deaths over the period contrasts with a slight reduction in daily active case numbers over the period.
Understanding the variations in epidemic parameters
With more resources, it would make sense to model different settings separately, and then combine them. If (as it is) the reproduction number R0<1 for the community, the population at large (although varying by location, environment etc), but higher in hospitals, and even higher in Care Homes, then these scenarios would have different transmission rates in the model, different effectiveness of counter-measures, and differences in several other parameters of the model(s). Today the CSA (Sir Patrick Vallance) stated that indeed, there is to be a randomised survey of people in different places (geographically) and situations (travel, work etc) to work out where the R-value is in different parts of the population.
But I have continued with the means at my disposal (the excellent basis for modelling in Alex Visscher’s paper that I have been using for some time).
Ultimately, as I said I my article at https://www.briansutton.uk/?p=1595, a multi-phase model will be needed (as per Imperial College and Harvard models illustrated here:-
and I am sure that it is the Imperial College version of this (by Neil Ferguson and his team) that will be to the forefront in that advice. The models looks at variations in policy regarding different aspects of the lockdown interventions, and the response of the epidemic to them. This leads to the cyclicity illustrated above.
In my model, the rate of deaths is the most accurately available data, (even though the basis for reporting it has just changed) and the model fit is based on that. I have incorporated that reporting update into the model.
Up to lockdown (March 23rd in the UK, day 51), an infection transmission rate k11 (rate of infection of previously uninfected people by those in the infected compartment) and a correction factor are used to get this fit for the model as close as possible prior to the intervention date. For example, k11 can be adjusted, as part of a combination of infection rates; k12 from sick (S) people, k13 from seriously sick (SS) people and k14 from recovering (B, better) people to the uninfected community (U). All of those sub-rates could be adjusted in the model, and taken together define the overall rate of transition of people from from Unifected to Infected.
After lockdown, the various interventions – social distancing, school and large event closures, restaurant and pub closures and all the rest – are represented by an intervention effectiveness percentage, and this is modified (as an average across all those settings I mentioned before) to get the fit of the model after the lockdown measures as close as possible to the reported data, up to the current date.
I had been using an intervention effectiveness of 90% latterly, as the UK community response to the Government’s advice has been pretty good.
But with the UK Government move to include data from other settings (particularly the Care Home setting) I have had to reduce that overall percentage to 85% (having modelled several options from 80% upwards) to match the increased reported historic death rate.
It is, of course, more realistic to include all settings in the reported numbers, and in fact my model was predicting on that basis at the start. Now we have a few more weeks of data, and all the reported data, not just some of it, I am more confident that my original forecast for 39,000 deaths in the UK (for this single phase outlook) is currently a better estimate than the update I made a week or so ago (with 90% intervention effectiveness) to 29,000 deaths in the Model Refinement article referred to above, when I was trying to fit just hospital deaths (having no other reference point at that time).
Here are the charts for 85% intervention effectiveness; two for the long term outlook, into 2021, and two up until today’s date (with yesterday’s data):
Another output would be for UK cases, and I’ll just summarise with these charts for all cases up until June 2020 (where the modelled case numbers just begin to level off in the model):-
As we can see, the fit here isn’t as good, but this also reflects the fact that the data is less certain than for deaths, and is collected in many different ways across the UK, in the four home countries, and in the conurbations, counties and councils that input to the figures. I will probably have to adjust the model again within a few days, but the outlook, long term, of the model is for 2.6 million cases of all types. We’ll see…
Outlook beyond the Lockdown – again
I’m modest about my forecasts, but the methodology shows me the kind of advice the Government will be getting. The behavioural “science” part of the advice (not in the model) taking the public “tiredness” into account, was the reason for starting partial lockdown later, wasn’t it?
It would be more of the same if we pause the wrong aspects of lockdown too early for these reasons. Somehow the public have to “get” the rate of infection point into their heads, and that you can be infecting people before you have symptoms yourself. The presentation of the R number in today’s Government update might help that awareness. My article on R0 refers
Neil Ferguson of Imperial College was publishing papers at least as far back as 2006 on the mitigation of flu epidemics by such lockdown means, modelling very similar non-pharmaceutical methods of controlling infection rates – social distancing, school closures, no public meetings and all the rest. Here is the 2006 paper, just one of 188 publications over the years by Ferguson and his team. https://www.nature.com/articles/nature04795
The following material is very recent, and, of course, focused on the current pandemic. https://www.imperial.ac.uk/…/Imperial-College-COVID19…
All countries would have been aware of this from the thinking around MERS, SARS and other outbreaks. We have a LOT of prepared models to fall back on.
As other commentators have said, Neil Ferguson has HUGE influence with the UK Government. I’m not sure how quickly UK scientists themselves were off the mark (as well as Government). We have moved from “herd immunity” and “flattening the curve” as mantras, to controlling the rate of infection by the measures we currently have in place, the type of lockdown that other countries were already using (in Europe, Italy did that two weeks before we did, although Government is saying that we did it earlier in the life of the epidemic here in the UK).
One or two advisory scientists have broken ranks (John Edmunds reported at https://www.reuters.com/…/special-report-johnson… ) on this to say that the various Committees should have been faster with their firm advice to Govenment. Who knows?
But what is clear from the public pronouncements is that Governments are now VERY aware of the issue of further peaks in the epidemic, and I would be very surprised to see rapid or significant change in the lockdown (it already allows some freedoms here in the UK, not there in some other countries, for example exercise outings once a day). I wouldn’t welcome being even more socially distanced than others, as a fit 70+ year-old person, through the policy of shielding, but if it has to be done, so be it.