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Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 29)

Published
3 December 2020
From
Director-General Health and Social Care
Directorate
Constitution Directorate
Part of
Coronavirus (COVID-19) in Scotland
ISBN
9781800044029

Latest findings in modelling the COVID-19 epidemic in Scotland, both in terms of the spread of the disease through the population (epidemiological modelling) and of the demands it will place on the system, for example in terms of health care requirement.

This document is part of a collection

View supporting documents Supporting documents

What the modelling tells us about the epidemic as a whole

Figure 1 shows how Rt has changed since February (including 50% and 95% confidence intervals). Before the “stay at home” restrictions were put in place Rt was above 1, and most likely to have been between 3 and 4 before any interventions were put in place.

Figure 1: Trends in R t for Scotland, 2020.
Graph showing the trends in the Rt value for Scotland over time, as calculated by the model. The graph shows step changes downwards at the point when each intervention was introduced. This figure shows Rt fell below 1.0 on the 23rd of March, when the “stay at home” advice was given. The Rt has been above 1 since around the time the school summer holidays ended.

Source: Scottish Government modelled estimates using Imperial College model code; actual data from https://www.nrscotland.gov.uk/statistics-and-data/statistics/statistics-by-theme/vital-events/general-publications/weekly-and-monthly-data-on-births-and-deaths/deaths-involving-coronavirus-covid-19-in-scotland

The various groups which report to the Scientific Pandemic Influenza Group on Modelling (SPI-M) use different sources of data in their models (i.e. deaths, hospital admissions, cases) so their estimates of R are also based on these different methods. SAGE’s consensus view across these methods, as of 02 December, was that the value of Rt in Scotland was between 0.8 and 1.0. The R value estimated by the Scottish Government is within the consensus range (Figure 2).

Figure 2. Estimates of R t for Scotland, as of 02 December, including 90% confidence intervals, produced by SAGE. The blue bars are death-based models, purple use multiple sources of data and cyan use Covid‑19 test results. The estimate produced by the Scottish Government (a semi-mechanistic model) is the 3 rd from left (yellow), while the SAGE consensus range is the right-most (red).
A graph showing the range of values which each of the academic groups reporting an R value to SAGE are likely to lie within, as of 2 December. The blue bars (first and second from left, 2nd from right) are death-based models, purple (5th to 10th from the left) use multiple sources of data. The estimate produced by the Scottish Government (a deaths-based model) is the 3rd from left (yellow). The R value estimated by the Scottish Government is similar to the estimates of other groups using models which draw upon numbers of deaths. The SAGE consensus, shown at the right hand side of the plot, is that the most likely “true” range is between 0.8 and 1.0.

Source: Scientific Advisory Group for Emergencies (SAGE).

The various groups which report to the Scientific Pandemic Influenza Group on Modelling (SPI-M) use different sources of data in their models to produce estimates of incidence (Figure 3). SPI-M’s consensus view across these methods, as of 02 December, was that the incidence of new daily infections in Scotland was between 44 and 82 new infections per 100,000. This equates to between 2,400 and 4,500 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as of 02 December, including 90% confidence intervals, produced by SPI-M. The blue bars are death-based models and the purple bars represent models which use multiple sources of data. The estimate produced by the Scottish Government (a semi-mechanistic model) is the 3 rd from left (yellow), while the SAGE consensus range is the right-most (red).
A graph showing the ranges the values which each of the academic groups in SPI-M are reporting for incidence (new daily infections per 100,000) are likely to lie within, as of 02 December. The blue bars are death based models (1st and 2nd from left). The purple bars (4th to 7th from the left) use multiple sources of data. The estimate produced by the Scottish Government (a deaths-based model) is the 3rd from the left (yellow). The SAGE consensus (44 to 82 new daily infections per 100,000) is shown at the right hand side of the plot.

Source: Scientific Pandemic Influenza Group on Modelling (SPI-M).

The consensus from SAGE for this week is that the growth rate in Scotland is between -3% and -1% per day. Last week the growth rate was in the range -3% and 0%.

Figure 4 shows the epidemiological model forecasts of daily deaths produced by the Scottish Government, given the present set of interventions.

Figure 4. Scottish Government short-term forecast of the number of deaths from Covid-19 in Scotland, based on actual data (to 24 November).
Bar chart showing daily numbers of deaths caused by Covid-19 in Scotland between 12 March and 24 November, 2020. Overlain on this is the “estimated deaths” result from the model, which smooths out the cyclical weekly pattern in the reported numbers, due to fewer deaths being registered over a weekend.

Source: Scottish Government modelled estimates using Imperial College model code; actual data from https://www.nrscotland.gov.uk/statistics-and-data/statistics/statistics-by-theme/vital-events/general-publications/weekly-and-monthly-data-on-births-and-deaths/deaths-involving-coronavirus-covid-19-in-scotland

The logistical model developed by Scottish Government to assess implications for health care demand (see previous Research Findings) has been adapted to produce a short/medium-term predictions of infections.

Figure 5 shows a “Lower” projection, which assumes the Rt value is currently slightly below 1 and there will be limited increase in transmission from winter conditions, and a “Higher” projection, which assumes that Rt is currently slightly higher (but still below 1), and it will increase as winter sets in.

Figure 5. Short term forecast of modelled total new infections, adjusting positive tests to account for asymptomatic and undetected infections, from Scottish Government modelling, positive test data up to 28 November.
Line graph showing the two week ahead lower and higher scenario predictions using the logistics model to extend the estimated number of infections from the Imperial College model in a manner that fits with the number of actual cases. The higher scenario indicates over 3,500 infections, whereas the lower scenario indicates over 1,500 infections in two weeks.

Contact

Email: modellingcoronavirus@gov.scot

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