Model update for the latest UK Coronavirus numbers

Introduction and summary

This is a brief update to my UK model predictions in the light of a week’s published data regarding Covid-19 cases and deaths in all settings – hospitals, care homes and the community – rather than just hospitals and the community, as previously.

In order to get the best fit between the model and the published data, I have had to reduce the effectiveness of interventions (lockdown, social distancing, home working etc) from 85% last week ( in my post immediately following the Government change of reporting basis) to 84.1% at present.

This reflects the fact that care homes, new to the numbers, seem to influence the critical R0 number upwards on average, and it might be that R0 is between .7 and .9, which is uncomfortably near to 1. It is already higher in hospitals than in the community, but the care home figures in the last week have increased R0 on average. See my post on the SIR model and importance of R0 to review the meaning of R0.

Predicted cases are now at 2.8 million (not reflecting the published data, but an estimate of the underlying real cases) with fatalities at 42,000.

Possible model upgrades

The Government have said that they are to sample people randomly in different settings (hospital, care homes and the community), and regionally, better to understand how the transmission rate, and the influence on the R0 reproductive number, differs in those settings, and also in different parts of the UK.

Ideally a model would forecast the pandemic growth on the basis of these individually, and then aggregate them, and I’m sure the Government advisers will be doing that. As for my model, I am adjusting overall parameters for the whole population on an average basis at this point.

Another model upgrade which has already been made by academics at Imperial College and at Harvard is to explore the cyclical behaviour of partial relaxations of the different lockdown components, to model the response of the pandemic to these (a probable increase in growth to some extent) and then a re-tightening of lockdown measures to cope with that, followed by another fall in transmission rates; and then repeating this loop into 2021 and 2022, showing a cyclical behaviour of the pandemic (excluding any pharmaceutical (e.g. vaccine and medicinal) measures). I covered this in my previous article on exit strategy.

This explains Government reluctance to promise any significant easing of lockdown in any specific timescales.

Current predictions

My UK model (based on the work of Prof. Alex Visscher at Concordia University in Montreal for other countries) is calibrated on the most accurate published data up to the lockdown date, March 23rd, which is the data on daily deaths in the UK.

Once that fit of the model to the known data has been achieved, by adjusting the assumed transmission rates, the data for deaths after lockdown – the intervention – is matched by adjusting parameters reflecting the assumed effectiveness of the intervention measures.

Data on cases is not so accurate by a long way, and examples from “captive” communities indicate that deaths vs. cases run at about 1.5% (e.g. the Diamond Princess cruise ship data).

The Italy experience also plays into this relationship between deaths and actual (as opposed to published) case numbers – it is thought that a) only a single figure percentage of people ever get tested (8% was Alex’s figure), and b) again in Italy, the death rate was probably higher than 1.5% because their health service couldn’t cope for a while, with insufficient ICU provision.

In the model, allowing for that 8%, a factor of 12.5 is applied to public total and active cases data, to reflect the likely under-reporting of case data, since there are relatively few tests.

In the model, once the fit to known data (particularly deaths to date) is made as close as possible, then the model is run over whatever timescale is desired, to look at its predictions for cases and deaths – at present a short-term forecast to June 2020, and a longer term outlook well into 2021, by when outcomes in the model have stabilised.

Model charts for deaths

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The fit of the model here can be managed well, post lockdown, by adjusting the percentage effectiveness of the intervention measure, and this is currently set at 84.1%. This model predicts fatalities in the UK at 42,000. They are reported currently (8th May 2020) at 31241.

Model charts for cases

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As we can see here, the fit for cases isn’t as good, but the uncertainty in case number reporting accuracy, owing to the low level of testing, and the variable experience from other countries such as Italy, means that this is an innately less reliable basis for forecasting. The model prediction for the outcome of UK case numbers is 2.8 million.

If testing, tracking and tracing is launched effectively in the UK, then this would enable a better basis for predictions for case numbers than we currently have.

Conclusions?!

I’m certainly not at a concluding stage yet. A more complex model is probably necessary to predict the situation, once variations to the current lockdown measures begin to happen, likely over the coming month or two in the first instance.

Models are being developed and released by research groups, such as that being developed by the RAMP initiative at https://epcced.github.io/ramp/

Academics from many institutions are involved, and I will take a look at the models being released to see if they address the two points I mentioned here: the variability of R0 across settings and geography, and the cyclical behaviour of the pandemic in response to lockdown variations.

At the least, perhaps, my current model might be enhanced to allow a time-dependent interv_success variable, instead of a constant lockdown effectiveness representation.