Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 9)

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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Contents
Coronavirus (COVID-19): modelling the epidemic (issue no. 9)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 9)

9 page PDF

547.0 kB

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 9)

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 9 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 10 July there were around 60 new infections and 700 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 15 July, R in Scotland was estimated to be between 0.5 & 0.9.
  • These forecasts were based on estimates of moving in to phase 2 guidance, implemented from 18 June. Changes associated with the move to phase 3 will not be fully seen until early August. 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 R t 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 15 July, was that the value of Rt in Scotland was between 0.5 and 0.9.

Figure 2. Estimates of R t for Scotland, as of 15 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 0.5 and 0.9.

Source: Scientific Advisory Group for Emergencies (SAGE).

The Scottish Government's epidemiological model estimates that on 10July there were around 60 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 700 (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

840

670

1,050

22 May

580

450

730

29 May

410

320

530

05 June

290

220

380

12 June

210

150

280

19 June

150

100

210

26 June

110

70

150

03 July

80

50

120

10 July

60

40

90

17 July

40

20

70

24 July

30

20

50

Table 2: Estimated number of people in Scotland who could be infectious.

Estimated Infectious Pool

Date

Mid

Lower

Upper

Percentage Weekly Change

15 May

10,700

8,600

13,300

-

22 May

7,400

5,900

9,300

-30%

29 May

5,200

4,000

6,600

-30%

05 June

3,700

2,800

4,700

-29%

12 June

2,600

1,900

3,500

-29%

19 June

1,900

1,300

2,500

-29%

26 June

1,300

900

1,900

-28%

03 July

1,000

600

1,400

-28%

10 July

700

400

1,000

-28%

17 July

500

300

800

-26%

24 July

400

200

600

-26%

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 (10 July).
A barchart showing daily numbers of deaths caused by Covid-19 in Scotland between 12th March and 10th 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 forecast of hospital beds required by Covid 19 patients in Scotland over the next two weeks is not included this week, as the numbers have fallen to a low level. Should these numbers begin to rise significantly this forecast will be reintroduced.

The 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 3 in our modelling until early August.

The medium-term forecasts produced by the Scottish Government (Figure 4 and 5) using the logistics model show 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 6 and 7).

The three scenarios presented in Figures 4 and 5 for hospital demand and Figure 6 and 7 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 5 and 7.

The number of hospital beds in use (Figure 4) is tracking above the worse scenario. This is likely to be due to Covid patients remaining in hospital for longer than expected.

Figure 4: Logistical model medium term forecast of the total number of people requiring a hospital bed from Covid-19 in Scotland, 10 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 100 in early July, to below 30 at the beginning of 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. Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

Figure 5: Logistical model medium term forecast of admissions of people requiring a hospital bed from Covid-19 in Scotland, 10 July.
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 6 in early July, to below 3 at the beginning of August. The actual number of admissions is falling, but tracking below model predictions.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code. Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

Figure 6: Logistical model medium term forecast of total number of people requiring an intensive care bed from Covid-19 in Scotland, 10 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 10 in early July, to less than 3 at the beginning of August.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code. Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

Figure 7: Logistical model medium term forecast of admissions of people requiring an intensive care bed from Covid-19 in Scotland, 10 July.
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 every 2 days in early July, to around 1 every 5 days at the beginning of August.

Source: Scottish Government modelled estimates using outputs from the Imperial College model code. Actual data from https://www.gov.scot/publications/coronavirus-covid-19-trends-in-daily-data/

What next?

The modelled estimates of the numbers of new cases and infectious people, along with how this relates to hospital and ICU requirements
will be published each week. Where appropriate, Rt will also be provided. Further information can be found at https://www.gov.scot/coronavirus-covid-19


Contact

Email: modellingcoronavirus@gov.scot