Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 67)

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. 67)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 67)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 67)

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 26th August 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 1.3 and 1.6, with the growth rate between 5% and 10%.

The number of new cases has continued to increase over the last week. The estimate of R has continued to increase, and has the highest upper limit since October 2020.

R is an indicator that lags by two to three weeks and therefore should not be expected to reflect recent fluctuations, such as the increase in reported cases that has been seen in the last two weeks.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 1.3 and 1.6. This is an increase in the lower and upper limits from last week, and is the highest upper limit of R since October 2020.
  • The number of new daily infections for Scotland is estimated as being between 73 and 138, per 100,000 people. This is an increase in the lower and upper limits since last week.
  • The growth rate for Scotland is currently estimated as between 5% and 10% This is an increase in the lower and upper limits since last week. The upper limit is at the highest level since September 2020.
  • Average contacts have increased by approximately 33% in the last two weeks (comparing surveys pertaining to 12th August - 18th August and 26th August - 1st September) with a current level of 5.1 daily contacts.
  • Mean contacts within the work setting have at least doubled in the last two weeks. There has also been a rise in mean contacts within the home and other setting (contacts outside of the home, school and work), increasing by 6% and 11% respectively.
  • All age groups with the exception of those aged 30-39 have had an rise in contacts within the last two weeks. Increases across the age groups are largely driven by a rise in contacts within the work setting.
  • The highest interactions within age groups remain between those 18-29 with each other. The biggest increase in interactions in the last two weeks is seen between those 18-29 with those under 18.
  • The proportion of individuals wearing a face covering where they have at least one contact outside of the home remains at a similar level to two weeks prior, currently at 82%.
  • Hospitalisations are now rising. Future hospital occupancy and intensive care use are likely to continue rising as infections rise.
  • Modelled rates of positive tests per 100K using data to 27th August indicate that, for the week commencing 12th September 2021, there are 29 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability.
  • Of these, 12 local authorities are expected to exceed 500 cases per 100k with at least 75% probability. These are Dumfries & Galloway, East Dunbartonshire, East Renfrewshire, Falkirk, Glasgow, North Ayrshire, North Lanarkshire, Renfrewshire, South Ayrshire, South Lanarkshire, West Dunbartonshire and West Lothian.
  • Two local authorities (North Lanarkshire and South Lanarkshire) are expected to exceed 1000 cases per 100k with at least 75% probability.
  • Nationwide, levels of Covid-19 in wastewater have risen by around 30% since the previous week. In the week prior to this, levels approximately doubled.
  • Covid-19 levels in wastewater are currently at the highest reported since the start of the pandemic.
  • Modelling of Long Covid gives estimates that on 19th September 2021 between 0.8% and 2.2% of the population are projected to experience symptoms for 12 weeks or more after their first suspected Covid infection in Scotland. This is an increase in the upper limit from last week.

Recent cases

Figure 1 shows the number of cases reported in Scotland between May and September 2021. 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 reported in Scotland to 2nd September 2021
Figure 1. A chart showing the number of cases reported in Scotland between May and September, and the cut off points for each of the modelling inputs.

R, growth rate and incidence are as of 17th August (dashed line 1). This report covers the period up to 27th August for wastewater analysis and the modelled rates of positive tests per 100k (dashed line 2). The medium term projections by the Scottish Government of infections, hospitalisations and ICU beds, the contact patterns and the long Covid analysis use data to 1st September (dashed line 3).

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 UK Health Security Agency (UKHSA) 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 to estimate the proportion of cases that will require hospital, and the length of time people that people will stay there.

What the modelling tells us about the epidemic as a whole

The R value and growth rates are estimated by several independent modelling groups based in universities, Public Health England (PHE) and the Joint Biosecurity Centre. Estimates are considered, discussed and combined at the Epidemiology Modelling Review Group (EMRG), which sits within the UKHSA.

UKHSA's consensus view across these methods, was that the value of R as at 17th August[1] in Scotland was between 1.3 and 1.6 (see Figure 2)[2].

R is an indicator that lags by two to three weeks and therefore should not be expected to reflect recent fluctuations, such as the increase in reported cases that has been seen in the last two weeks.

This week the Scottish Government presented two outputs to EMRG. The first uses confirmed cases as published by Public Health Scotland (PHS), and deaths from National Records Scotland (NRS). The second uses instead wastewater data to estimate the number of cases, and deaths from NRS. Both outputs are shown in Figures 2 and 3.

Figure 2. Estimates of R t for Scotland, as of 17th August, including 90% confidence intervals, produced by EMRG [3].
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.

Source: EMRG

The various groups which report to the EMRG use different sources of data in their models to produce estimates of incidence (Figure 3). UKHSA's consensus view across these methods, as at 17th August, was that the incidence of new daily infections in Scotland was between 73 and 138 new infections per 100,000. This equates to between 4,000 and 7,500 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as at 17th August, including 90% confidence intervals, produced by EMRG 2.
Figure 3. 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: EMRG

The consensus from UKHSA for this week is that the growth rate in Scotland is between 5% and 10% per day as at 17th August. The lower and upper limits have increased since last week. The upper limit is at the highest level since September 2020.

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

Average contacts have increased by approximately 33% in the last two weeks (comparing surveys pertaining to 12th August - 18th August and 26th August - 1st September) with a current level of 5.1 daily contacts as seen in Figure 4. Mean contacts within the work setting have at least doubled in the last two weeks. There has also been a rise in mean contacts within the home and other setting (contacts outside of the home, school and work), increasing by 6% and 11% respectively.

Figure 4: Mean Adult Contacts (truncated at 100) from SCS.
Figure 4. 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. All age groups with the exception of those aged 30-39 have had a rise in contacts within the last two weeks. Increases across the age groups are largely driven by a rise in contacts within the work setting.

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

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 12th August - 18th August and 26th August - 1st September and the difference between these periods. The highest interactions between age groups remain between those 18‑29 with each other. The biggest increase in interactions in the last two weeks is seen between those 18-29 with those under 18.

Figure 6: Overall mean contacts by age group before for the weeks relating to 12th August - 18th August and 26th August - 1st September.
Figure 6. Heat maps showing the mean contacts by age group in the weeks of 12 August and 26 August.

As seen in Figure 7, the proportion of participants visiting different locations remains at similar levels across the majority of locations with those using public transport and also individuals visiting a work place reporting the biggest increase. The proportion of participants using public transport increased from approximately 21% to 25% with participants visiting a work place increasing from 15% to 18% in the last two weeks.

Figure 7: Locations visited by participants at least once for panel A and B (from SCS).
Figure 7. A series of line graphs showing locations visited by participants at least once for panel A and B in various settings.

Figure 8 shows the number of people wearing a face covering where they have at least one contact outside of the home. This remains at a similar level to two weeks prior, currently at 82%.

Figure 8: Proportion of adults wearing a face covering over time (with at least one contact outside of the home).
Figure 8. A line chart showing the proportion of adults wearing a face covering ove time (with at least one contact outside the home)

Vaccinations and contacts patterns

From Figure 9, it can be seen that the older age groups have similar levels of contacts but higher vaccinations than the youngest age group, they also have the lowest weekly case number comparatively to the younger age groups. Despite that they have higher weekly hospitalization levels and deaths to that seen with the younger age groups.

Figure 9: Average contacts for Panel B, weekly cases, covid-19 hospital admissions and deaths [4] and cumulative vaccinations by age band [5]
Figure 9. 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 10 shows three projections over the three weeks to 19th September.

'Worse - continues' assumes that transmission increases, and this results in accelerating growth in infections. 'Better - continues' assumes transmission remains at the current level. 'Better - drops' assumes that transmission will return to previous levels over the next week[6].

Figure 10. Medium term projections of modelled total new daily infections, adjusting positive tests [7] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 1st September.
Figure 10. A line graph showing the short term forecast of modelled new infections.

There is uncertainty as to how much infections will increase or decrease in coming weeks.

Figure 11 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.

Hospital and ICU occupancies are rising. The scale of any future increase in hospital occupancy and intensive care use is highly uncertain, and depends on the number of infections.

Figure 11. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 1st September.
Figure 11. A line graph showing the short term forecast of hospital bed demand.

Figure 12 shows the impact of the projection on ICU bed demand.

Figure 12. Medium term projections of modelled ICU bed demand, from Scottish Government modelling [8], based on positive test data reported up to 1st September.
Figure 12. 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.

What the modelling tells us about projections of hospitalisations and deaths in the medium term

SPI-M produces projections of the epidemic[9] (Figures 13 and 14), combining estimates from several independent models (including the Scottish Government's logistics modelling, as shown in Figures 10-12). These projections are not forecasts or predictions. They represent a scenario in which the trajectory of the epidemic continues to follow the trends that were seen in the data up to 27th August and do not include the effects of any future policy or behavioural changes.

The delay between infection, developing symptoms, the need for hospital care, and death means they cannot fully reflect the impact of behaviour changes in the two to three weeks prior to 27th August. Projecting forwards is difficult when the numbers of admissions and deaths fall to very low levels, which can result in wider credible intervals reflecting greater uncertainty. The interquartile range can be used, with judgement, as the projection from which estimates may be derived until the 21st September, albeit at lower confidence than the 90% credible interval.

These projections include the potential impact of vaccinations over the next few weeks. Modelling groups have used their expert judgement and evidence from Public Health England, Scottish Universities & Public Health Scotland, and other published efficacy studies when making assumptions about vaccine effectiveness.

Figure 13. SPI-M medium-term projection of daily hospitalisations in Scotland, at 50% and 90% credible intervals.
Figure 13. A combination scatter and line chart, showing the SAGE medium term projection of hospitalisations against the actual hospitalisations.
Figure 14. SPI-M medium-term projection of daily deaths in Scotland, including 50% and 90% credible intervals.
Figure 14. A combination scatter and line chart, showing the SAGE medium term projection of deaths against the actual deaths.

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 30th August 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.

Because infections may still be rising rapidly in some areas, the local projections may not fully reflect this.

Modelled rates of positive tests per 100K using data to 27th August (Figure 15) indicate that, for the week commencing 12th September 2021, there are 29 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability[10].

Of these, 12 local authorities are expected to exceed 500 cases per 100k with at least 75% probability. These are Dumfries & Galloway, East Dunbartonshire, East Renfrewshire, Falkirk, Glasgow, North Ayrshire, North Lanarkshire, Renfrewshire, South Ayrshire, South Lanarkshire, West Dunbartonshire and West Lothian.

Two local authorities (North Lanarkshire and South Lanarkshire) are expected to exceed 1000 cases per 100k with at least 75% probability[11].

Figure 15. Probability of local authority areas exceeding thresholds of cases per 100K (12th to 18th September 2021), data to 27th August.
Figure 15. A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (12th to 18th September 2021).

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

Levels of Covid-19 in wastewater collected at a number of sites around Scotland are adjusted for population and local changes in intake flow rate and compared to 7-day average daily new case rates derived from Local Authority and Neighbourhood (Intermediate Zone) level aggregate data. See Technical Annex in Issue 34 of these Research Findings for the methodology.

Nationwide, levels of wastewater (WW) Covid-19 have risen to around 110 million gene copies per person per day (Mgc/p/d). While this represents a smaller rate of increase than last week, this means WW virus levels are currently at the highest levels since the start of the pandemic.

Figure 16 shows the national weekly aggregate for the original 28 sites (sampled from August 2020, in blue) and, from January 2021, the aggregate for the full set of 110 sampled sites (in green), with a small number of unrealistically large outliers excluded. With national average new case rates (smoothed by a 7 day running mean) also shown, a large and rapid increase is seen in both measures. WW in particular rose by around 30%, leading to levels exceeding the previous record high set in early July.

Figure 16. National average trends in wastewater Covid-19 and daily new case rates (7 day moving average) [12].
Figure 16. A line chart showing national average trends in wastewater Covid-19 and daily case rates.

Figure 17 uses colours to map (i) the local authority average WW viral Covid-19 levels (in Mgc/p/d) over the two-week period from 14th August to 27th August, and (ii) the change in viral Covid-19 levels compared to the previous two-week period 31st July to 13th August. This map shows that large increases are seen in most local authorities[13]. In particular, for the Highlands local authority area, the increasing levels seen is mostly due to trends at the single large site of Allanfearn in Inverness-shire, while Galashiels explains most of the increase seen in the Scottish Borders.

Figure 17. Map showing wastewater Covid-19 levels (million gene copies/person/day) for each local authority for 14th August to 27th August and changes relative to 31st July to 13th August. White areas show local authorities without sufficient data to display.
Figure 17. Two maps showing the wastewater Covid-19 levels for each local authority. The first map shows the levels between 14th and 27th August, and the second shows differences from the previous two weeks.

As usual, there is some variability amongst the sites. To mitigate the effect of reduced sampling, in Figure 19 we aggregate together subgroups of sites according to the population they cover. In this view, we see a fairly consistent pattern where sites covering small populations (which are typically more isolated rural sites) show lower levels of Covid‑19 activity than others. However, in both groups of sites, WW Covid-19 levels have risen dramatically recently. Levels in the smaller sites are about 70% of the other sites.

Figure 18. Average trends in wastewater Covid-19, with some anomalies removed as in Figure 10. As well as the national average in black, WW average viral levels are also given for the smaller sites in red (that cover under 10k inhabitants) and largest sites in blue (that cover over 100k inhabitants).
Figure 18. A line chart showing average trends in wastewater Covid-19 and daily case rates, split by population size.

What estimates do we have of the number of people experiencing long Covid symptoms?

The Scottish Government is modelling the number of people likely to experience long Covid symptoms. This has been projected to estimate long Covid rates in the future, based on Scottish Government medium term projection modelling, as set out in Figure 19.

This modelling estimates that at 19th September 2021 between 44,000 (0.8% of the population) and 118,000 (2.2%) people are projected to experience symptoms for 12 weeks or more after their first suspected Covid infection in Scotland.

These are preliminary results, further data on rates of long Covid and associated syndromes as research emerges are required.

Figure 19: Estimates of long Covid prevalence at 12 weeks from 16th February 2020 to 19th September 2021 for the 5th and 25th percentile better long Covid rates (showing 95% confidence intervals). ONS estimates with range also shown.
Figure 19. A percentile chart showing the estimated number of long Covid prevalence at 12 weeks, compared to ONS estimates.

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