Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 66)

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. 66)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 66)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 66)

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 19th 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 1.0 and 1.3, with the growth rate between -1% and 6%, based on the period up to 23rd August.

The number of new cases has continued to increase over the last week. The estimate of R has increased to above 1.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 1.0 and 1.3, based on the period up to 23rd August. This is an increase in the lower and upper limits from last week, is now clearly above 1, and is the highest upper limit of R since 12th July 2021.
  • The number of new daily infections for Scotland is estimated as being between 45 and 125, per 100,000 people, based on the period up to 23rd August. This is an increase in the lower and upper limits since last week.
  • The growth rate for Scotland is currently estimated as between -1% and 6%, based on the period up to 23rd August. This is an increase in the lower and upper limits since last week.
  • Average contacts have increased by 15% in the last two weeks (comparing surveys pertaining to 5th August - 11th August and 19th August - 25th August) with a current level of 4.7 daily contacts.
  • Contacts within the work have increased by approximately 64% compared to two weeks prior. Contacts within the home and other settings (contacts outside of the home, school and work) have remained at similar levels over the same period.
  • All age groups with the exception of those aged 18-29 have had an rise in contacts within the last two week, with those aged 30-39 approximately doubling. Increases across the age groups are largely driven by a rise in contacts within the work setting.
  • The biggest increase in interactions is seen between those 30-39 with those under 18.
  • Visits to a work place have increased from approximately 14% to 19% with individuals visiting a pub or restaurant increasing from 46% to 49% in the last two weeks.
  • 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 23rd August indicate that, for the week commencing 5th September 2021, there are 28 local authorities which are expected to exceed 100 cases per 100k with at least 75% probability.
  • Of these, twelve local authorities are expected to exceed 300 cases per 100k with at least 75% probability. These are Argyll & Bute, Edinburgh, Dumfries & Galloway, East Dunbartonshire, East Renfrewshire, Glasgow, North Ayrshire, North Lanarkshire, Renfrewshire, South Lanarkshire, West Dunbartonshire and West Lothian.
  • Only one local authority, Dumfries & Galloway, is expected to exceed 500 cases per 100k with at least 75% probability.
  • Nationwide, the latest levels of wastewater Covid-19 RNA have approximately doubled since the previous week.
  • Wastewater Covid-19 RNA concentrations are now approaching the maximum level reached during the peak in July 2021. The rise in wastewater has been greatest in the central belt and the south.
  • Modelling of Long Covid gives estimates that on 12th September 2021 between 0.8% and 2.1% 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 August 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 26th August 2021
A chart showing the number of cases reported in Scotland between May and August, and the cut off points for each of the modelling inputs.

This report covers the period up to 20th August for wastewater analysis (indicated by dashed line 1). The estimates of R, incidence, growth rates, the modelled rates of positive tests per 100k, and the long Covid analysis use data to 23rd August (dashed line 2). The medium term projections by the Scottish Government of infections, hospitalisations and ICU beds, and the contact patterns use data to 25th August (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[1] 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 as of 25th August, using data to 23rd August, was that the value of R in Scotland was between 1.0 and 1.3 (see Figure 2)[2].

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. Both outputs are shown in Figures 2 and 3. Note that as the former model includes deaths, it is returning a lower R value than the latter model where deaths are not included.

Figure 2: Estimates of R t for Scotland, as of 25th August, including 90% confidence intervals, produced by EMRG [3]. Data to 23rd August.
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, using data to

23rd August, was that the incidence of new daily infections in Scotland was between 45 and 125 new infections per 100,000. This equates to between 2,500 and 6,800 people becoming infected each day in Scotland.

Figure 3: Estimates of incidence for Scotland, as of 25th August, including 90% confidence intervals, produced by EMRG [2]. Data to 23rd August.
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 -1% and 6% per day using data to 23rd August. The lower and upper limits have increased since last week.

What we know about who is testing positive with Covid

The Early Pandemic Evaluation and Enhanced Surveillance of Covid-19 (EAVE) 2 Study Group[4] has updated the pattern of demographics and clinical risk groups over time for those who tested positive in Scotland (see Technical Annex in issue 34 of the Research Findings).

Figure 4 gives the age group, risk group and vaccination status of those first testing positive in the period 7th to 13th August 2021 and linking into the EAVE cohort. Vaccine status is a simple binary classification denoting that the individual had at least one dose of the vaccine before testing positive (vaccinated) or was unvaccinated at the time of testing positive. Risk group status is the number of Q-Covid[5] risk groups to which a person belongs.

One quarter of those testing positive are under 18, 50% are aged under 30 and only 6% aged 65+[6]. Among those aged under 18 the vast majority are unvaccinated while among those aged 18-29 just over half of them are vaccinated, most will just have had one dose. Very few individuals testing positive under 40 have multiple co-morbid conditions (0.2% of all cases were under 40 and had 3 or more co morbid conditions). The majority of those aged over 40 are vaccinated when testing positive, and most will have had two doses of vaccine, but a relatively small proportion are in the groups most at risk of a severe outcome. Among those testing positive 1.5% are aged 65+ and have 4 or more co-morbid conditions.

Figure 4: Proportion of positive tests, by age group, clinical risk group and vaccination status for the week beginning 7th August 2021. [7]
A bar chart showing the proportion of positive tests by age group, clinical risk group and vaccination status for the week beginning 7th August.

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

Average contacts have increased by 15% in the last two weeks (comparing surveys pertaining to 5th August - 11th August and 19th August - 25th August) with a current level of 4.7 daily contacts as seen in Figure 5. Contacts within the work have increased by approximately 64% compared to two weeks prior. Contacts within the home and other setting (contacts outside of the home, school and work) have remained at similar levels over the same period.

Figure 5: 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 6 shows how contacts change across age group and setting. All age groups with the exception of those aged 18-29 have had an rise in contacts within the last two week, with those aged 30-39 approximately doubling. Increases across the age groups are largely driven by a rise in contacts within the work setting.

Figure 6: 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 August 2021.

The heatmaps in Figure 7 show the mean overall contacts between age groups for the weeks relating to 5th August - 11th August and 19th August - 25th August and the difference between these periods. The biggest increase in interactions is seen between those 30-39 with those under 18.

Figure 7: Overall mean contacts by age group before for the weeks relating to 5th August - 11th August and 19th August - 25th August.
Heat maps showing the mean contacts by age group in the weeks of 22 July and 5 August.

As seen in Figure 8, the proportion of participants visiting different locations remains at similar levels across the majority of locations with those visiting a work place and also those visiting a pub or restaurant reporting the biggest increase in attendance. Visits to a work place have increased from approximately 14% to 19% with individuals visiting a pub or restaurant increasing from 46% to 49% in the last two weeks.

Figure 8: 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.

Figure 9 shows the proportion of participants that reported contacts had indoors and outdoors for contacts individually reported for panel A. A contact can be recorded as both indoor and outdoor. The graph also shows contacts reported as outside only and indoor only. The proportion of contacts reported to have been indoors only has increased slightly within the last two weeks, from 55% to 58%.

Figure 9: Proportion of participants reported indoors and outdoors for contacts individually reported for panel A.
A line chart showing the proportion of contacts reported indoors, outdoors or both.

Figure 10 shows the number of people wearing a face covering where they have at least one contact outside of the home. This has increased from 78% to 84% in the last two weeks.

Figure 10: Proportion of adults wearing a face coverings over time (with at least one contact outside of the home).
A line chart showing the proportion of adults wearing a face covering over time (with at least one contact outside the home)

Vaccinations and contacts patterns

From Figure 11, 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, which are currently rising. Despite that they have higher weekly hospitalization levels and deaths to that seen with the younger age groups.

Figure 11: Average contacts for Panel A, weekly cases, covid-19 hospital admissions and deaths [8] and cumulative vaccinations by age band [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 12 shows three projections over the three weeks to 12th 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 the recent increase in transmission is short-lived, and it will return to previous levels[10].

Figure 12: Medium term projections of modelled total new daily infections, adjusting positive tests [11] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 25th August.
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. This will drive how much hospital beds and intensive care beds will rise.

Figure 13 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, and the future increase or decrease in hospital occupancy and intensive care use is highly uncertain, and depends on the number of infections.

Figure 13: Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 25th August.
A line graph showing the short term forecast of hospital bed demand

Figure 14 shows the impact of the projection on ICU bed demand.

Figure 14: Medium term projections of modelled ICU bed demand, from Scottish Government modelling [12], based on positive test data reported up to 25th August.
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[13] (Figure 15), combining estimates from several independent models (including the Scottish Government's logistics modelling, as shown in Figures 12-14). 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 23rd 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 23rd 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 7th 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 15: SPI-M medium-term projection of daily hospitalisations in Scotland, including 50% and 90% credible intervals.
A combination scatter and line chart, showing the SAGE medium term projection of hospitalisations against the actual hospitalisations.

We are not projecting the numbers of people expected to die with Covid‑19 this week. The number of daily deaths remains at low levels.

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 23rd 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 of the recent increase in cases, infections may be rising rapidly and that the local projections have yet to fully reflect this.

Modelled rates of positive tests per 100K using data to 23rd August (Figure 16) indicate that, for the week commencing 5th September 2021, there are 28 local authorities which are expected to exceed 100 cases per 100k with at least 75% probability[14].

Of these, twelve local authorities are expected to exceed 300 cases per 100k with at least 75% probability. These are Argyll & Bute, Edinburgh, Dumfries & Galloway, East Dunbartonshire, East Renfrewshire, Glasgow, North Ayrshire, North Lanarkshire, Renfrewshire, South Lanarkshire, West Dunbartonshire and West Lothian.

Only one local authority, Dumfries & Galloway, is expected to exceed 500 cases per 100k with at least 75% probability[15].

Figure 16: Probability of local authority areas exceeding thresholds of cases per 100K (5th to 11th September 2021), data to 23rd August.
A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (5th to 11th September 2021).

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

Levels of Covid-19 RNA 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, the latest levels of wastewater (WW) Covid-19 RNA have approximately doubled since the previous week and averaged around 90 million gene copies per person per day (Mgc/p/d) for the week 14th to 20th August, compared to 42 Mgc/p/d the previous week.

Figure 17 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. Both WW Covid-19 concentrations and cases are now approaching the maximum level reached during the peak in July 2021.

Figure 17: National average trends in wastewater Covid-19 and daily new case rates (7 day moving average) [16].
A line chart showing national average trends in wastewater Covid-19 and daily case rates.

Figure 18 uses colours to map (i) the local authority average WW viral Covid-19 levels (in Mgc/p/d) over the two-week period from 7th August to 20th August, and (ii) the change in viral Covid-19 levels compared to the previous two-week period 24th July to 6th August. This shows that the rise has been greatest in the central belt and the south.

Figure 18: Map showing wastewater Covid-19 levels (million gene copies/person/day) for each local authority for 7th August to 20th August and changes relative to 24th July to 6th August. Areas shown in white have insufficient data available for the relevant period [17].
Two maps showing the wastewater Covid-19 levels for each local authority. The first map shows the levels between 7th and 20th August, and the second shows differences from the previous two weeks.

The increase in both WW Covid-19 concentrations and cases is especially marked in the area covered by the NHS Greater Glasgow and Clyde health board (Figure 19), where the most recent WW measurements at the sites at Dalmuir, Shieldhall, Dalmarnock and Paisley all show a sharp rise. However, increases are also starting to appear in other parts of Scotland, for example at Nigg in Aberdeen (Figure 20).

Figure 19: Average trends in wastewater Covid-19 and daily case rates (7 day moving average) in NHS Greater Glasgow and Clyde Health Board (pop: 1147 k).
A line chart showing average trends in wastewater Covid-19 and daily case rates for NHS Greater Glasgow and Clyde.
Figure 20: Wastewater Covid-19 and daily case rate (7 day moving average) for Nigg (covered pop: 218k) in Aberdeen [18].
A line chart showing average trends in wastewater Covid-19 and daily case rates for Nigg in Aberdeen.

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 21.

This modelling estimates that at 12th September 2021 between 43,000 (0.8% of the population) and 115,000 (2.1%) people 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 since last week.

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

Figure 21: Estimates of long Covid prevalence at 12 weeks from 16th February 2020 to 12th September 2021 for the 5th and 25th percentile better long Covid rates (showing 95% confidence intervals). ONS estimates with range also shown.
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