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Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 16)

Published
3 September 2020
Directorate
Constitution Directorate
Topic
Coronavirus (COVID-19) in Scotland, Public safety and emergencies
ISBN
9781800040441

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.

View supporting documents Supporting documents

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 16)

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 27 August 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.

This edition of the research findings focuses on the epidemic as a whole, looking at estimates of R, it also looks at whether certain parts of Scotland are exceeding the number of cases which we would expect at this point in the epidemic, and then goes on to introduce improved modelling based on how many contacts people have with one another.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.9 and 1.4.
  • The growth rate for Scotland is estimated as being between -1% and +8%.
  • The number of new daily infections for Scotland is estimated as being between 1 and 6 per 100,000 people.
  • There were 10 local authority areas which exceeded what would be expected at this stage in the epidemic between 25-31 August. Glasgow City, Renfrewshire, East Dunbartonshire, Clackmannanshire, South Ayrshire, West Dunbartonshire, South Stirling, Scottish Borders, East Renfrewshire and City of Edinburgh were areas of higher risk of transmission

Overview of Scottish Government Modelling

Epidemiology is the study of how diseases spread within populations. One way we do this is using our best understanding of the way the infection is passed on and how it affects people who catch it to create mathematical simulations. Because people who catch Covid-19 have a relatively long period in which they can pass it on to others before they begin to have symptoms, and the majority of people infected with the virus will experience mild symptoms, this "epidemiological modelling" provides insights into the epidemic that cannot easily be measured through testing e.g. of those with symptoms, as it estimates the total number of new daily infections and infectious people, including those who are asymptomatic or have mild symptoms.

Modelling also allows us to make short-term forecasts of what may happen with a degree of uncertainty. These can be used in health care and other planning. The modelling in this research findings is undertaken using different types of data which going forward aims to both model the progress of the epidemic in Scotland and provide early indications of where any changes are taking place.

Firstly, modelling outputs are provided here on the current epidemic in Scotland as a whole, based on a range of methods. Because it takes a little over three weeks on average for a person who catches Covid-19 to show symptoms, become sick, and either die or recover, there is a time lag in what this model can tell us about any re-emergence of the epidemic and where in Scotland this might occur. However modelling of Covid deaths is an important measure of where Scotland lies in its epidemic as a whole. In addition the modelling groups which feed into the SAGE consensus use a range of other data along with deaths in their estimates of R and growth rate. These outputs are provided in the first part of this research findings. This week the type of data used in each model to estimate R is highlighted in Figure 2.

Secondly, modelling is provided this week around whether the number of positive test results we are seeing exceeds what would be expected. This replaces the short-term modelling of NHS capacity provided in these reports previously, as the focus at this stage of the epidemic is around identifying any possible re-emergence of the virus in Scotland rather than whether there is sufficient hospital capacity to treat large numbers of Covid cases.

What the modelling tells us about the epidemic as a whole

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
Figure 1. 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 fell 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; 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 2 September, was that the value of Rt in Scotland was between 0.9 and 1.4. The R value estimated by the Scottish Government falls within this range, and is similar to the estimates of other groups using models which draw upon numbers of deaths (Figure 2).

Figure 2. Estimates of R t for Scotland, as of 2 September, 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 deaths-based model) is the 4th from left (yellow), while the SAGE consensus range is the right-most (red).
Figure 2. 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 2nd September. The blue bars (first to third from the left, second from right) are death-based models, purple (5th to 8th from the left) use multiple sources of data and cyan (9th and 10th from the left) use Covid-19 test results. The estimate produced by the Scottish Government (a deaths-based model) is the 4th from left (yellow) and is around 0.85. 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 0.9 and 1.4.

Source: Scientific Advisory Group for Emergencies (SAGE).

On the 1 September, Public Health Scotland recorded 154[1] new confirmed positive cases, with 506 total positive new cases over the week of 25-31 August. At this point in the epidemic, with very low numbers of deaths to inform its outputs, the results of our model have begun to underestimate prevalence and incidence.

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. SPI-M's consensus view across these methods, as of 2 September, was that the incidence of new daily infections in Scotland was between 1 and 6 new infections per 100,000. The incidence value estimated by the Scottish Government falls within this range. This equates to between 60 – 330 people becoming infected each day in Scotland. Given the level of asymptomatic infected people, 154 confirmed new cases remains within this range.

Figure 3. Estimates of incidence for Scotland, as of 2 September, including 90% confidence intervals, produced by SPI-M. 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 deaths-based model) is the 3rd from left (yellow), while the SAGE consensus range is the right-most (red).
Figure 3. A graph showing the range of values which each of the academic groups in SPI-M reporting an incidence (new daily cases per 100,000) value are likely to lie within, as of 2nd September. The blue bars (at the left hand side of the plot) are death-based models, purple (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 incidence value estimated by the Scottish Government is within the range of 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 and 6.

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 -1% and +8% per day. This is an increase, compared to last week, where growth rate was in the range -7% to +1%.

Figure 4 shows the epidemiological model forecasts of daily deaths produced by the Scottish Government, given the present set of interventions. This measure of the epidemic is forecast to remain near zero in the weeks ahead.

Figure 4. Scottish Government short-term forecast of the number of deaths from Covid-19 in Scotland, based on actual data (18 August).
Figure 4. A bar chart showing daily numbers of deaths caused by Covid-19 in Scotland between 12th March and 27th August, 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

What the modelling tells us about whether Covid infections exceeded what would be expected at this stage in the epidemic

While metrics such as the reproductive rate - the R number - have been useful in guiding our response to Coronavirus so far, the models we use rely on numbers of deaths to track the epidemic. These have fallen to low levels, which means we need to find new ways to monitor trends in the epidemic. One of the ways we can do this is to calculate whether the number of confirmed infections (based on testing) in each area exceeds the number that was expected, given the number recorded across the country - this is called "exceedance". An analysis of trends across Local Authorities in Scotland has been developed by modellers at the University of Warwick on behalf of the Scottish Government.

Numbers of positive tests recorded each day, adjusted for population of each local authority and number of cases seen in preceding weeks, should fall within a certain distribution of values, which will rise and fall depending on the number of cases being seen nationally. Areas where the number of positive test results fall beyond the upper 95th percentile of this distribution may be at risk of seeing increased local transmission of Covid and heightened vigilance may be required. This happens when the cumulative exceedance is higher than 6.0.

In the week preceding 31August, across Scotland the epidemic in Scotland was driven by the outbreak in the greater Glasgow area (Figure 5). Recent cumulative exceedance highlights Glasgow City (exceedance = 9.8), Renfrewshire (8.5), East Dunbartonshire (5.3), Clackmannanshire (5.1), South Ayrshire (4.5), West Dunbartonshire (4.4), South Stirling (3.7), Scottish Borders (3.7), East Renfrewshire (3.6) and City of Edinburgh (3.4) as areas of higher risk of transmission (Figure 6).

Figure 5. Map of cumulative exceedance, 31 August, for Scottish Local Authorities.
Figure 5. A choropleth map of Scotland, divided into Local Authority areas. The shading colour of each Local Authority area is determined by the recent cumulative exceedance at 31st August. Glasgow City is shown to have the highest exceedance of any Local Authority.
Figure 6. Graphs of daily and cumulative exceedance for the local authorities deemed as higher risk over the period 25 – 31 August.
Figure 6. Graphs showing the daily and cumulative exceedance for the local authorities of Glasgow City, Renfrewshire, East Dunbartonshire, Clackmannanshire, South Ayrshire, West Dunbartonshire, Stirling, Scottish Borders, East Renfrewshire and the City of Edinburgh from 9th August 2020 to 31st August 2020.

What next?

Most models are based on the number of daily deaths, however as the numbers of deaths in Scotland are now at low levels, and as deaths happen sometime after people become ill (around three weeks), it is important to have models that pick up immediate upturns in the post-peak phase of the epidemic.

The Scottish Government has also been working with a number of academic modelling groups to develop other estimates of the epidemic in Scotland. Recently, we introduced the Exceedance method developed by the University of Warwick, and next week we hope to introduce a new way of measuring the epidemic which is based on a survey of people's behaviours, rather than numbers of cases or deaths.

The London School of Hygiene and Tropical Medicine have developed a modelling technique called "CoMix" which is based on how may contact people have each week. The contacts people have are collected via an online survey. Until now Scotland has been included in their modelling but represented by around 10% of respondents (under 150 people) leading to a high level of uncertainty in the results. Scottish Government are now running a Scottish survey to boost these numbers to over 3,000 people, the "COVID-19 online research panel". The outputs of the model will provide alternative measures of the epidemic at the time (e.g. R number) and will provide an early indication of a resurgence in the virus. Having a range of different types of models for Scotland is the best chance of spotting an upturn in cases and help us plan what to do if this happens.

The modelled estimates of the numbers of new cases and infectious people will continue to be provided as measures of the epidemic as a whole, along with measures of the current point in the epidemic such as exceedance. Rt and growth rate will also be provided. Further information can be found at https://www.gov.scot/coronavirus-covid-19.

Contact

Email: modellingcoronavirus@gov.scot

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