Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (Issue No. 65)

Published: 20 Aug 2021

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. 65)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 65)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 65)

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 13th 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 0.8 and 1.1, with the growth rate between -3% and 1%, based on the period up to 16th August.

The number of new cases has been increasing over the last week, with a marked increase on the 18th and 19th August. The estimate of R has increased and now span one. However, admissions to hospital and ICU have continued to decline over the last week.

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 week.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.8 and 1.1, based on the period up to 16th August. This is an increase in the lower and upper limits from last week.
  • The number of new daily infections for Scotland is estimated as being between 34 and 64, per 100,000 people, based on the period up to 16th August.
  • The growth rate for Scotland is currently estimated as between -3% and 1%, based on the period up to 16th August.
  • Average contacts have remained at a similar level in the last two weeks (comparing surveys pertaining to 22nd July - 28th July and 5th August - 11th August) with a current level of 4.1 daily contacts.
  • Contacts within the work and home setting have decreased compared to two weeks prior, by 9% and 8% respectively, whereas contacts within the other setting (contacts outside of the work, school and home) have increased slightly by 5%.
  • The biggest increase in interactions in the last two weeks is seen between those aged 18-29 with those under 18.
  • Visits to a non-essential shop have increased from approximately 40% to 44% with individuals attending a hairdressers/beautician increasing from 10% to 14% in the last two weeks.
  • The proportion of contacts reported to have been indoors only has increased within the last two weeks whereas the proportion of contacts occurring outside only has shown a decrease over the same period.
  • Hospitalisations have been declining from a peak in mid-July, but have now levelled off. Potential future changes in hospital occupancy and intensive care use depend on both current infection levels and the impact of the recent relaxations of measures which will take a few weeks to become apparent.
  • Modelled rates of positive tests per 100K using data to 16th August indicate that, for the week commencing 29th August 2021, 28 local authorities are expected to exceed 50 cases per 100k with at least 75% probability.
  • Of these, 8 local authorities are expected to exceed 100 cases per 100k with at least 75% probability. These are Dumfries & Galloway, Fife, Glasgow, Inverclyde, North Ayrshire, North Lanarkshire, Renfrewshire and South Lanarkshire.
  • Overall, wastewater (WW) Covid-19 RNA concentrations rose from the previous week similar to the observed rise in the rate of new cases. However, levels were rising substantially at the end of the period at many sites.
  • Comparing the last two days of WW measurements (since 13th August) to measurements immediately prior, an increase in WW viral RNA is seen in 19 out of the 22 sites with available data. The increase is of a large magnitude, doubling or tripling the level in many sites.
  • The number of people likely to experience long Covid symptoms on 5th September 2021 is estimated to be between 0.8% and 2.0% of the population, an increase since 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 19th August 2021
Figure 1. 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 11th August for contact patterns (indicated by dashed line 1). The estimates of R, incidence, growth rates, the modelled rates of positive tests per 100k, wastewater analysis, and the long Covid analysis use data to 16th August (dashed line 2). The medium term projections by the Scottish Government of infections, hospitalisations and ICU beds uses data to 18th 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.

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.

R is an indicator that lags by two to three weeks[2] and therefore should not be expected to reflect recent fluctuations, such as the increase in reported cases that has been seen in the last week.

UKHSA's consensus view across these methods as of 18th August, using data to 9th August, was that the value of R in Scotland was between 0.8 and 1.1 (see Figure 2)[3].

This week the Scottish Government presented two outputs to EMRG. 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 18th August, including 90% confidence intervals, produced by EMRG [4]. Data to 16th August.
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, using data to

16th August, was that the incidence of new daily infections in Scotland was between 34 and 64 new infections per 100,000. This equates to between 1,900 and 3,500 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as of 18th August, including 90% confidence intervals, produced by EMRG 2. Data to 16th August.
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 -3% and 1% per day using data to 16th August. The lower and upper limits have increased since last week.

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

Average contacts have remained at a similar level in the last two weeks (comparing surveys pertaining to 22nd July - 28th July and 5th August - 11th August) with a current level of 4.1 daily contacts as seen in Figure 4. Contacts within the work and home setting have decreased compared to two weeks prior, by 9% and 8% respectively, whereas contacts within the other setting (contacts outside of the work, school and home) have increased slightly by 5%.

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. Those aged 18-29 have shown the biggest increase in contacts within the last two weeks, increasing by 25%, which is largely driven by a rise in contacts within the other setting. All remaining age groups have either had a reduction in overall contacts or remained at a similar level in comparison to two weeks prior.

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 August 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 22nd July - 28th July and 5th August - 11th August and the difference between these periods. The biggest increase in interactions in the last two weeks is seen between those aged 18-29 with those under 18.

Figure 6: Overall mean contacts by age group before for the weeks relating to 22nd July - 28th July and 5th August - 11th August.
Figure 6. Heat maps showing the mean contacts by age group in the weeks of 22 July and 5 August.

As seen in Figure 7, the proportion of participants visiting different locations remains at similar levels across the majority of locations with those visiting a non-essential shop and also those visiting a hairdressers/beautician reporting the biggest increase in attendance. Visits to a non-essential shop have increased from approximately 40% to 44% with individuals attending a hairdressers/beautician increasing from 10% to 14% 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 illustrates the proportion of all reported contacts that were indoors, outdoors or covered both settings. 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 within the last two weeks whereas the proportion of contacts occurring outside only has shown a decrease over the same period.

Figure 8: Proportion of participants reported indoors and outdoors for contacts individually reported for panel A.
Figure 8. A line chart showing the proportion of contacts reported indoors, outdoors or both.

Vaccinations and contacts patterns

From Figure 9, it can be seen that the older age groups have fewer contacts and more 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 this, the older age groups have similar or higher hospitalization levels and deaths to that seen with the younger age groups.

Figure 9: Average contacts for Panel A, weekly cases, covid-19 hospital admissions and deaths [5] and cumulative vaccinations by age band [6]
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 5th September.

'Worse' assumes that increasing transmission continues for the next two weeks. 'Better' assumes transmission remains at the current level after the recent uptick in cases. 'No uptick' projects forward at the previous level of transmission from before the recent uptick[7].

Figure 10. Medium term projections of modelled total new daily infections, adjusting positive tests [8] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 18th August.
Figure 10. A line graph showing the short term forecast of modelled new infections.

There is uncertainty as to how much infections will increase in coming weeks. This will drive how much hospital beds and intensive care beds will rise.

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 have stopped falling, and the future increase or decrease in hospital occupancy and intensive care use is highly uncertain, and depends on both current infection levels and the impact of the relaxation of restrictions.

Figure 11. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 18th August.
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 [9], based on positive test data reported up to 18th August.
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[10] (Figure 13), 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 16th 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 16th 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 13. SPI-M medium-term projection of daily hospitalisations in Scotland, including 50% and 90% credible intervals.

Figure 13. SPI-M medium-term projection of daily hospitalisations in Scotland, including 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.

We are not projecting the numbers of people expected to die with Covid‑19 this week. The number of daily deaths has fallen to very 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 16th 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.

As noted, this week there has been an uptick in cases. The potential that this could be a strong and sudden uptick in the data, rather than statistical noise, is reflected in the very high upper bounds on the confidence intervals this week. It is therefore recommended that while the average projections remain low, there is an initial signal that case numbers may be rising rapidly and that the projections have yet to fully reflect this.

Modelled rates of positive tests per 100K using data to 16th August (Figure 14) indicate that, for the week commencing 29th August 2021, there are 28 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability[11].

Of these, eight local authorities are expected to exceed 100 cases per 100k with at least 75% probability. These are Dumfries & Galloway, Fife, Glasgow, Inverclyde, North Ayrshire, North Lanarkshire, Renfrewshire and South Lanarkshire[12].

Figure 14. Probability of local authority areas exceeding thresholds of cases per 100K (29th August to 4th September 2021), data to 16th August.
Figure 14. A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (29th August to 4th 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 averaged around 42 million gene copies per person per day (Mgc/p/d) for the week, representing a rise from last week. To note, levels were rising substantially at the end of the period at many sites.

Figure 15 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. For this aggregate measure, nationally WW Covid-19 concentrations rose modestly from the previous week similar to the observed rise in the rate of new cases.

The temporary decrease in the number of samples tested continues this week, which impacts on the frequency of observations and the population covered by sampling, especially amongst smaller sites. This means there should be particular caution in interpreting the local authority results in Table 2 in the Technical Annex[13].

Figure 15. National average trends in wastewater Covid-19 and daily new case rates (7 day moving average) [14].
Figure 15. A line chart showing national average trends in wastewater Covid-19 and daily case rates.

While the rise shown in Figure 15 is relatively modest, averaging over weeks masks the extent of increases in the most recent measurements. Comparing the last two days of WW measurements (since 13th August) to measurements immediately prior, an increase in WW viral Covid-19 is seen in 19 out of the 22 sites with available data. The increase is also large in magnitude, frequently doubling or tripling the level. While in many sites, there is only a single measurement available, at Seafield (covering the Edinburgh), shown in Figure 16, multiple measurements have been registered in the vicinity of 60 Mgc/p/d. At Shieldhall and Dalmuir in Glasgow, a similar recent rise was seen, though less data is currently available there.

While Seafield (Figure 16) has been quite variable in terms of WW levels in recent weeks, locations like Meadowhead (Figure 17) show a clearer increase over the same timescale. Several other sites give similar results.

Further measurements are required to establish whether this signal is sustained.

Figure 16. Wastewater Covid-19 and daily case rate (7 day moving average) for Seafield (covered pop: 606k) in Edinburgh [15].
Figure 16. A line chart showing average trends in wastewater Covid-19 and daily case rates for Seafield in Edinburgh.

Figure 17. Wastewater Covid-19 and daily case rate (7 day moving average) for Meadowhead (covered pop: 191k) in South Ayrshire.

Figure 17. Wastewater Covid-19 and daily case rate (7 day moving average) for Meadowhead (covered pop: 191k) in South Ayrshire.
Figure 17. A line chart showing average trends in wastewater Covid-19 and daily case rates for Meadowhead in South Ayrshire.

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 18.

This modelling estimates that at 5th September 2021 between 41,000 (0.7% of the population) and 110,000 (2.0%) people were projected to experience symptoms for 12 weeks or more after their first suspected Covid infection in Scotland. This is an increase since last week.

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

Figure 18: Estimates of long Covid prevalence at 12 weeks from 16th February 2020 to 5th September 2021 for the 5th and 25th percentile better long Covid rates (showing 95% confidence intervals). ONS estimates with range also shown.
Figure 18. 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