Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 58)

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.

Coronavirus (COVID-19): modelling the epidemic (issue no. 58)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 58)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 58)

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 25th June 2021. The estimates in this document help the Scottish Government, the health service and the wider public sector plan and put into 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, growth rate and incidence as well as local measures of change in the epidemic.

In Scotland, the modelled estimate for R is between 1.2 and 1.5, with the growth rate between 3% and 7% based on the period up to 28th June. The R and growth rate indicators lag by two to three weeks, as a result the estimates cannot fully reflect the significant increase in daily cases seen over the past week.

Based on the most recent increase in cases, infections, hospital beds and ICU are projected to rise – for how long this continues is uncertain.

Following the recent increase in cases, we are projecting a continued growth in the epidemic in Scotland, with considerable uncertainty as to what this means for future weeks.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 1.2 and 1.5, based on the period up to 28th June. This has increased since last week.
  • The number of new daily infections for Scotland is estimated as being between 48 and 76, per 100,000 people, based on the period up to 28th June.
  • The growth rate for Scotland is currently estimated as being between 3% and 7%, based on the period up to 28th June. This has increased since last week.
  • Average contacts have increased slightly (6%) in the last two weeks (comparing surveys pertaining to 3rd June - 9th June and 17th June - 23rd June) with a current level of 4.6 daily contacts.
  • Contacts within the school setting are 3 times higher than reported two weeks prior and contacts within the other setting (contacts outside of the school, home and work) have increased by 7%. Average contacts within the home and work setting have remained at similar levels over the same period.
  • Those aged under 40 have shown the biggest increase in mean contacts in the last two weeks, increasing by at least 33%. These increases are largely driven by contacts had within the school and work settings. Average contacts for those aged over 70 have also increased, although to a lesser extent (15%), which is influenced by an increase in contacts within a school or other (contacts outside of the school work or home) setting.
  • The biggest increase in interactions is seen with those aged between 18-39 with those aged under 18 whereas those aged between 40-49 have reported the biggest reductions in interactions with those under 18.
  • The biggest increase in the proportion of participants visiting different locations, though slight, is seen in those visiting a pub or restaurant and those using public transport. Visits to pub or restaurant has increased from approximately 37% to 39% with individuals using public transport increasing from 16% to 19% in the last two weeks.
  • Based on the recent increase in cases, infections, hospital beds and ICU are projected to rise – for how long this continues is uncertain.
  • Modelled rates of positive tests per 100K using data to 28th June indicate that for the week commencing 11th July 2021, there are 28 local authorities with at least a 75% probability of exceeding 150 cases.
  • Of these, 19 local authorities have at least a 75% probability of exceeding 500 cases per 100k. These are Aberdeen, Aberdeenshire, Angus, Edinburgh, Dundee, East Ayrshire, East Dunbartonshire, East Lothian, Falkirk, Fife, Glasgow, Midlothian, North Ayrshire, North Lanarkshire, Perth and Kinross, Renfrewshire, South Lanarkshire, West Dunbartonshire and West Lothian.
  • Furthermore, there are 4 local authorities with at least a 75% probability of exceeding 1000 cases per 100k. These are Edinburgh, Dundee, Fife and Glasgow. Of these, Edinburgh is expected to exceed 2000 cases per 100k with at least a 75% probability
  • The overall level of wastewater (WW) Covid-19 rose rapidly in the last week.

Recent increase in cases

Figure 1 shows the number of cases reported in Scotland during May and June 2021, including the recent increase in cases seen in the last week. The vertical dashed lines indicate the cut off points for each of the modelling inputs; after these dates, the number of cases is not incorporated into the outputs.

Figure 1: Cases in reported in Scotland to 30th June 2021
A chart showing the number of cases reported in Scotland in May and June, and the cut off points for each of the modelling inputs.

This report covers the period up to 23rd June for contact patterns (indicated by dashed line 1). The estimates of R, incidence, growth rates, and for the modelled rates of positive tests per 100k use data to 28th June (dashed line 2). Wastewater data is provided to 29th June (dashed line 3). Medium term projections by the Scottish Government of infections, hospitalisations and ICU beds have been calculated using data to 30th June based on date reported (dashed line 4).

Overview of Scottish Government Modelling

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 our model can tell us about any re-emergence of the epidemic and where in Scotland this might occur.

However modelling of Covid-19 deaths is an important measure of where Scotland lies in its epidemic as a whole. In addition, the modelling groups that feed into the SAGE consensus use a range of other data along with deaths in their estimates of R and the growth rate. These outputs are provided in this research findings. The type of data used in each model to estimate R is highlighted in Figure 2.

We use the Scottish Contact Survey (SCS) to inform a modelling technique based on the number of contacts between people. Over time, a greater proportion of the population will be vaccinated. This is likely to impact contact patterns and will become a greater part of the analysis going forwards.

The logistical model utilises results from the epidemiological modelling, principally the number of new infections. The results are split down by age group, and the model is used to give a projection of the number of people that will go to hospital, and potentially to ICU. This will continue to be based on both what we know about how different age groups are affected by the disease and the vaccination rate for those groups.

What the modelling tells us about the epidemic as a whole

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.

R is an indicator that lags by two to three weeks and therefore does not reflect any behavioural changes that have happened during this time. In particular, Scotland has seen a significant step change in the number of new daily cases over the past week and the associated R and growth rate estimates cannot fully reflect this; R in Scotland now is likely to be higher than that estimated here.

SAGE’s consensus view across these methods as of 30th June, using data to 28th June, was that the value of R in Scotland was between 1.2 and 1.5 (see Figure 2)[1].

This week the Scottish Government presented two outputs to SPI-M. The first uses confirmed cases as published by Public Health Scotland (PHS). The second uses instead wastewater data to estimate the number of cases. Both outputs are shown in Figures 2 and 3.

Figure 2. Estimates of R t for Scotland, as of 30th June, including 90% confidence intervals, produced by SAGE [2]. Data to 28th June.
A graph showing the range of values which each of the academic groups reporting an R value to SAGE are likely to lie within.

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, using data to 28th June, was that the incidence of new daily infections in Scotland was between 48 and 76 new infections per 100,000. This equates to between 2,600 and 4,200 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as of 30th June, including 90% confidence intervals, produced by SPI-M 2. Data to 28th June
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.

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 7% per day using data to 28th June.

What we know about how people’s contact patterns have changed

Average contacts have increased slightly (6%) in the last two weeks (comparing surveys pertaining to 3rd June - 9th June and 17th June - 23rd June) with a current level of 4.6 daily contacts as seen in Figure 4. Contacts within the school setting are 3 times higher than reported two weeks prior, and contacts within the other setting (contacts outside of the school, home and work) have increased by 7%. Average contacts within the home and work setting have remained at similar levels over the same period.

Figure 4: Mean Adult Contacts (truncated at 100) from SCS.
A line graph showing mean adult contacts in Scotland for Panel A and Panel B in the Scottish Contact Survey.

Figure 5 shows how contacts change across age group and setting. Those aged under 40 have shown the biggest increase in mean contacts in the last two weeks, increasing by at least 33%. These increases are largely driven by contacts had within the school and work settings. Average contacts for those aged over 70 have also increased, although to a lesser extent (15%), which is influenced by an increase in contacts within a school or other (contacts outside of the school work or home) setting. All remaining age groups have remained at similar levels or decreased within the last two weeks.

Figure 5: Average (mean) contacts for each panel per day by setting for adults in Scotland, truncated to 100 contacts per participant (from SCS).
A series of line graphs showing mean adult contacts by setting and age group for panel A and panel B from December 2020 to June 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 3rd June - 9th June and 17th June - 23rd June, and the difference between these periods. The biggest increase in interactions is seen with those aged between 18-39 with those aged under 18 whereas those aged between 40-49 have reported the biggest reductions in interactions with those under 18.

Figure 6: Overall mean contacts by age group before for the weeks relating to 3rd June - 9th June and 17th June - 23rd June.
Heat maps showing the mean contacts by age group in the weeks of 3 June and 17 June.
Figure 7: Locations visited by participants at least once for panel A and B (from SCS).
A series of line graphs showing locations visited by participants at least once for panel A and B in various settings.

The biggest increase in the proportion of participants visiting different locations, though slight, is seen in those visiting a pub or restaurant and those using public transport as seen in Figure 7. Visits to pub or restaurant has increased from approximately 37% to 39% with individuals using public transport increasing from 16% to 19% in the last two weeks.

Vaccinations and contacts patterns

From Figure 8, it can be seen that the older age groups have fewer contacts and more vaccinations than the younger age groups, they also have the lowest weekly case number comparatively to the younger age groups. Despite that, they have similar weekly hospitalization levels to that seen with the younger age groups.

Figure 8: Average contacts for Panel B, weekly cases, Covid-19 hospital admissions and deaths [3] and cumulative vaccinations by age band [4]
A series of line graphs showing average contacts, daily cases and deaths and cumulative vaccinations by age band.

What the modelling tells us about estimated infections as well as Hospital and ICU bed demand

The Scottish Government assesses the impact of Covid-19 on the NHS in the next few weeks in terms of estimated number of infections. Figure 9 shows two projections. ‘Worse’ is based on a continuation in transmission rate from last week’s level. ‘Better’ is based on a reduction, falling to below the level from before last week’s increase, due to school holidays[5].

In comparison to last week’s projections, the ‘Worse’ projection is lower and the ‘Better’ projection is higher. This is because we have more information and can therefore make a more precise estimate, narrowing the bounds of uncertainty somewhat. Nevertheless, the level of uncertainty remains high as we go into the summer holiday period.

Figure 9. Medium term projections of modelled total new infections, adjusting positive tests [6] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 30th June.
A line graph showing the short term forecast of modelled new infections.

There is uncertainty as to whether infections will continue to rise or will reduce in coming weeks. This will drive whether hospital beds and intensive care beds also continue to rise.

Figure 10 shows the impact of the projections on the number of people in hospital. The modelling includes all hospital stays, whereas the actuals only include stays up to 28 days duration that are linked to Covid-19. Work is ongoing to show the modelled occupancy for stays up to a 28 day limit.

The increase in cases seen in the last week is likely to lead to an increase in hospitalisations and intensive care use, with considerable uncertainty as to future weeks.

Figure 10. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 30th June.
A line graph showing the short term forecast of hospital bed demand.

Figure 11 shows the impact of the projection on ICU bed demand.

Figure 11. Medium term projections of modelled ICU bed demand, from Scottish Government modelling [7], based on positive test data reported up to 30th June.
A line graph showing a short term forecast of modelled ICU bed demand.

A comparison of the actual data against historical projections is included in the Technical Annex.

The delay between infection, developing symptoms, the need for hospital care, and death means SPI-M’s medium term projections will not fully reflect the impact of policy and behavioural changes made in the two to three weeks prior to 28th June. SPI-M does not have confidence that its projections reflect the recent and significant increase in cases in Scotland and has therefore decided not to produce consensus projections for Scotland this week.

What we know about which local authorities are likely to experience high levels of Covid-19 in two weeks’ time

We continue to use modelling based on Covid-19 cases and deaths using data to 28th June from several academic groups to give us an indication of whether a local authority is likely to experience high levels of Covid-19 in the future. This has been compiled via SPI-M into a consensus. In this an area is defined as a hotspot if the two week prediction of cases (positive tests) per 100K population is predicted to exceed a threshold, e.g. 500 cases.

Modelled rates of positive tests per 100K using data to 28th June (Figure 12) indicate that for the week commencing 11th July 2021, there are 28 local authorities with at least a 75% probability of exceeding 150 cases[8].

Of these, 19 local authorities have at least a 75% probability of exceeding 500 cases per 100k. These are Aberdeen, Aberdeenshire, Angus, Edinburgh, Dundee, East Ayrshire, East Dunbartonshire, East Lothian, Falkirk, Fife, Glasgow, Midlothian, North Ayrshire, North Lanarkshire, Perth and Kinross, Renfrewshire, South Lanarkshire, West Dunbartonshire and West Lothian.

There are 4 local authorities with at least a 75% probability of exceeding 1000 cases per 100k. these are Edinburgh, Dundee, Fife and Glasgow. Of these, Edinburgh is expected to exceed 2000 cases per 100k with at least a 75% probability[9].

Figure 12. Probability of local authority areas having more than 20, 50, 100, 150, 300, 500, 750, 1000 or 2000 cases per 100K (11th – 17th July 2021). Using data to 28th June.
A series of four maps showing the probability of local authority areas having more than 20, 50, 100, 150, 300, 500, 750, 1000 or 2000 cases per 100K (11th – 17th July 2021).

The local authority level modelling and national level modelling from SPI-M are based on different groups of models and look at different metrics. Furthermore the local level modelling is produced a day later than the national level. As a result, the local authority level and national level modelling do not exactly correspond to each other.

What can analysis of wastewater samples tell us about local outbreaks of Covid-19 infection?

Nationwide, wastewater (WW) COVID-19 RNA levels rose rapidly to around 47 million gene copies per person per day (Mgc/p/d), with the majority of the increase late in the week. Increases in levels occurred across a broad range of local authorities.

Figure 13 shows the national aggregate for the original 28 sites (in blue) and, from January 2021, the aggregate for the full set of sampled sites (in green), with a small number of unrealistically large outliers excluded. For case data, a large rise in cases occurred on June 21st (from around 30 new cases/100k per day to around 60), and so we show not just the usual 7 day running average but also the raw daily values (as unfilled circles) for the most recent data. A significant amount of increase is in the last few days (between 24th and 28th of June) of available data, increasing from around 24 to over 47 Mgc/p/d. The increase was especially large in the sites originally sampled, which tend to be larger sites.

Figure 13. National average trends in wastewater Covid-19 and daily case rates (7 day moving average) [10].
A line chart showing national average trends in wastewater Covid-19 and daily case rates.

What next?

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 Rt and the growth rate. Further information can be found at https://www.gov.scot/coronavirus-covid-19.

We may report on exceedance in future weeks when the background levels of Covid-19 reduces so that it can be useful in identifying outbreaks.


Contact

Email: modellingcoronavirus@gov.scot