Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 8)

Published: 9 Jul 2020

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.

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11 page PDF

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Contents
Coronavirus (COVID-19): modelling the epidemic (issue no. 8)
Coronavirus (COVID-19): Analysis - Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 8)

11 page PDF

750.3 kB

Coronavirus (COVID-19): Analysis - Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 8)

Background

This is a report on the Scottish Government modelling of the spread and level of Covid-19. This updates the previous publication on modelling of Covid-19 in Scotland published on the 2 July 2020. The estimates in this document help the Scottish Government, the health service and the wider public sector plan and put in place what is needed to keep us safe and treat people who have the virus, e.g. to decide how many Intensive Care Beds (ICU) we need available for Covid patients.

Key Points

  • Modelling is undertaken to look at the progression of the epidemic in Scotland and to inform the logistical response required.
  • This is done over two time periods. Short term, for the next two weeks, and longer term. Both of these help the Scottish Government and wider public sector plan their response and help determine if the measures in place are working.
  • Modelling by the Scottish Government estimates that on 3 July there were around 80 new infections and 1,000 people in Scotland who could be infectious with Covid-19. Both of these numbers have fallen significantly in the last week.
  • The modelling forecasts that the number of infectious people, the number of cases, hospital and ICU use and deaths are all likely to continue to fall over the next two weeks.
  • We currently use the value of R to talk about Covid-19 in Scotland. On 8 July, R in Scotland was estimated to be between 0.6 & 1.0.
  • These forecasts were based on estimates of moving in to phase 2 guidance, implemented from 18 June. Changes associated with the move to phase 2 will not be fully seen until mid-July. The longer term forecasts will be closely monitored against actual cases over the next few weeks as the situation changes.

The Imperial College modelling code used by the Scottish Government to understand the progression of the epidemic in Scotland is driven by changes in the numbers of deaths occurring each day. We have reached a point where this number is very low. While this is really good news, it makes reporting of the R number less helpful in understanding how the epidemic is changing. A small, localised outbreak would result in a high R value, even though the number of cases would actually be very few. If the number of deaths drops further we will likely report trends in the numbers of new cases, the numbers of people who may be infectious, and the rate of change of these figures.

What the modelling tells us

Figure 1 shows how Rt has changed since February. Before the “stay at home” restrictions were put in place Rt was above 1, and most likely to have been between 4 and 6 before any interventions were put in place.

Figure 1: Trends in Rt for Scotland, 2020
A 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 falling below 1.0 on the 23rd of March, when the “stay at home” advice was given.

Source: Scottish Government modelled estimates using Imperial College model code,

Source: 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 Rt value estimated by the Scottish Government falls within the range of values estimated by other modelling groups and considered by SPI-M and SAGE (Figure 2). SAGE’s consensus view, as of 8 July, was that the value of Rt in Scotland was between 0.6 and 1.0.

Figure 2. Estimates of Rt for Scotland, as of 8 July, including 90% confidence intervals, produced by SAGE. The estimate produced by the Scottish Government is the 6th 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. The SAGE consensus, shown at the right hand side of the plot, is that the most likely “true” range is between 0.6 and 1.0.

Source: Scientific Advisory Group for Emergencies (SAGE).

The Scottish Government’s epidemiological model estimates that on 3 July there were around 80 new cases of Covid-19 in Scotland (see Table 1), while the number of people in Scotland who could be infectious on this date was around 1,000 (see Table 2). Our estimates indicate this number has been declining by around 30% each week, and will continue to decline at a similar rate over the next two weeks.

Table 1: Estimated daily number of new Covid-19 cases in Scotland.
Estimated new daily infections
Date Mid Lower Upper
15 May 860 670 1,090
22 May 600 460 770
29 May 430 320 560
05 June 300 220 410
12 June 220 150 300
19 June 160 110 220
26 June 110 70 160
03 July 80 50 120
10 July 60 30 90
17 July 40 20 70
Table 2: Estimated number of people in Scotland who could be infectious.
Estimated Infectious Pool
Date Mid Lower Upper Percentage Weekly Change
15 May 10,900 8,600 15,500 -
22 May 7,600 5,900 11,000 -30%
29 May 5,300 4,100 7,800 -30%
05 June 3,800 2,800 5,600 -29%
12 June 2,700 2,000 4,100 -28%
19 June 1,900 1,400 3,000 -28%
26 June 1,400 900 2,300 -28%
03 July 1,000 600 1,700 -28%
10 July 700 400 1,200 -28%
17 July 500 300 900 -28%

Figure 3 shows the epidemiological model forecasts produced by the Scottish Government, given the present set of interventions. This epidemic curve continues to show signs of reducing.

Figure 3: Scottish Government short-term forecast of the number of deaths from Covid-19 in Scotland, based on actual data (3 July).
A barchart showing daily numbers of deaths caused by Covid-19 in Scotland between 12th March and 3rd July, 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. The model results suggest deaths in Scotland peaked around 19th April and have been steadily declining since then.

Source: Scottish Government modelled estimates using Imperial College model code,

Source: 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 short-term forecasts produced by SAGE suggested that the number of hospital beds occupied by Covid-19 patients in Scotland would fall over the last two weeks of June (Figure 4). This was well within our Covid-19 hospital capacity of 4,250.

The short and medium term forecasts presented here are fitted to trends in the historical data. Because it takes time for infected people to develop symptoms, require hospitalisation, and either die or recover, we will not fully see the effect of moving into phase 2 in our modelling until mid-July.

Figure 4. Short-term forecast of hospital bed occupancy in Scotland as produced by SAGE (25 June). This figure has not been updated this week.
A graph produced by the Scottish Government based on a short term forecast provided by SAGE of hospital bed occupancy by Covid-19 patients in Scotland. The most likely scenario shows occupancy declining from around 800 on 25th May to below 600 by 22nd June, and was forecast to decline at a similar rate over the following two weeks.

Source: This figure has been produced by the Scottish Government using the forecast data provided by SAGE.

The medium-term forecasts produced by the Scottish Government (Figure 5 and 6) using the logistics model show a similar story with a steady decline in the number of people requiring hospitalisation from Covid-19. The logistical model also provides us with a medium term forecast of the number of ICU beds which may be required (Figures 7 and 8).

The three scenarios presented in Figures 5 and 6 for hospital demand and Figure 7 and 8 for ICU demand are for different levels of daily infections. In each case, we translate these into logistical forecasts which are used for planning purposes.

The Worse and Better scenarios should not be considered an upper and lower bound respectively. It is important to note, in particular, that for planning reasons many of the assumptions used are deliberately precautionary, and so it is reassuring that actual case data are lower than the modelled estimate in the past, as is the case with the ICU admissions demand forecast in figures 6 and 8.

The number of hospital beds in use (Figure 5) is tracking above the worse scenario. This is likely to be due to Covid patients remaining in hospital for longer than expected.

Figure 5: Logistical model medium term forecast of the total number of people requiring a hospital bed from Covid-19 in Scotland, 3 July. Capacity is around 4,000.
A graph showing the modelled forecast of the most likely number of people in Scotland requiring a hospital bed due to Covid-19 in the longer term, along with better and worse case scenarios. In this figure, the most likely number of people requiring hospital treatment declines from around 200 in late June, to below 50 in August. The actual number of cases is falling at a similar rate, but tracking above model predictions.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code,

Source: Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

Figure 6: Logistical model medium term forecast of admissions of people requiring a hospital bed from Covid-19 in Scotland, 3 July. Capacity is around 4,000
A graph showing the modelled forecast of the most likely number of admissions of people in Scotland requiring a hospital bed due to Covid-19 in the longer term, along with better and worse case scenarios. In this figure, the most likely number of people admitted for hospital treatment declines from around 12 in late June, to below 3 in August. The actual number of cases is falling at a similar rate, but tracking below model predictions.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code,

Source: Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

Figure 7: Logistical model medium term forecast of total number of people requiring an intensive care bed from Covid-19 in Scotland, 3 July. Capacity is around 700.
A graph showing the modelled forecast of the most likely number of people in Scotland requiring intensive care due to Covid-19 in the longer term, along with better and worse case scenarios. In this figure, the most likely number of people requiring intensive care treatment declines from around 20 in late June, to around 5 in August.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code,

Source: Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

Figure 8: Logistical model medium term forecast of admissions of people requiring an intensive care bed from Covid-19 in Scotland, 3 July. Capacity is around 700.
A graph showing the modelled forecast of the most likely number of admissions of people in Scotland to intensive care due to Covid-19 in the longer term, along with better and worse case scenarios. In this figure, the most likely number of people admitted to intensive care treatment declines from around 1 per day in late June, to around 1 every 3 days in August.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code,

Source: Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

What next?

The modelled estimates of hospital and ICU use, and of the reproduction number Rt will be published each week. Further information can be found at https://www.gov.scot/coronavirus-covid-19


Contact

Email: modellingcoronavirus@gov.scot