Modelling Covid-19 or How Long will lockdown last?

The other day I went looking for all the open source data on Covid-19 in the UK so that I could do some modelling on when the peak was likely to be reached and, by inference, when we might hope to be able to resume normal activities.

When Will Lockdown End?

I’ll start with this, and you can ignore the caveats on why it’s nonsense (which is what always happens with mathematic models). If the assumptions are accurate (I can guarantee that they’re not), then by the end of July about 3 million people will have been infected and the first peak will have run its course. (See the graph below). If we’re lucky August will be party season!

caveats

• The data is incomplete, we’re only testing the sickest people who turn up in hospital, I’m not even certain that we’re testing everyone I’m hospital that might have Covid-19.
• There’s a massive time lag in the data we do have, people reported as testing positive today we’re probably infected over two weeks ago.
• There are obvious reporting anomalies in the data, you can see the weekends, so this makes it harder to identify trends and extrapolate.
• The open source data available only really tells us what happened in March.
• The margin of error is very large.

Building a Covid-19 Model

I’ve built lots of models for a variety of purposes. This one followed a method I’ve worked out from experience.

1. Get an understanding of the system you want to model
2. Work out what the outputs you need are
3. Collect appropriate input data
4. Look for relationships in the data
5. Build a model that uses relationships to show how inputs deliver outputs
6. Test the model against reality
7. Iterate

I built the model in a spreadsheet because that was the tool I had available on my personal machine. Discrete event simulation software might have been a better approach, but I don’t have that available right now.

Can You Build a Better Covid-19 Model?

In the interest of transparency here’s the spreadsheet that I built the model in, with all the data already in it. It’s a rough version, without much in the way of notes, but you can see the working if you are interested in this sort of thing. It’s not a work of beauty, I pulled it together in a few hours on Good Friday.

• covid-19 model v02 (ODS format)

Sources

• https://www.worldometers.info/coronavirus/country/uk/ – this draws on the Gov.UK daily info, but aggregates it and shows a time series. It’s really hard to find the daily figures from the UK government website for confirmed cases and reported hospital deaths.
• Table 11 of https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/weeklyprovisionalfiguresondeathsregisteredinenglandandwales from the ONS shows the Covid-19 registered deaths in England and Wales by the day that the person died.
• The Scots have the clearest data set for their registered deaths at https://www.nrscotland.gov.uk/covid19stats they are more up to date that ONS.

Assumptions

Some assumptions came out of the following articles.

Assumption	Value	Unit	Source
Incubation period (mean)	4	days	https://www.nejm.org/doi/full/10.1056/NEJMoa2002032
hospitalisation lag after symptoms	10	days	Unknown, range 7-10 days, couldn’t find peer-reviewed article.
Test result reporting lag (mean)	3	days	based on performance in NE Surrey, also reporting patterns
average time in hospital	13	days	https://www.nejm.org/doi/full/10.1056/NEJMoa2002032
Proportion needing hospitalisation	18.6%	of total cases	https://jamanetwork.com/journals/jama/fullarticle/2762130
Proportion needing critical care	4.7%	of total cases	https://jamanetwork.com/journals/jama/fullarticle/2762130
Proportion needing a ventilator	66.00%	of hospitalised	https://www.bmj.com/content/368/bmj.m1201
Median time in critical care	5	days	https://www.bmj.com/content/368/bmj.m1201
Time to conclusion (death or recovery)	23	days