Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 68)

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. 68)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 68)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 68)

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 2nd September 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%.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 1.2 and 1.5, as of 24th August. This is a decrease in the lower and upper limits from last week.
  • The number of new daily infections for Scotland is estimated as being between 118 and 214, 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 3% and 7% This is a decrease in the lower and upper limits since last week.
  • Average contacts have increased by approximately 14% in the last two weeks (comparing surveys pertaining to 19th August - 25th August and 2nd September - 8th September) with a current level of 5.3 daily contacts.
  • Mean contacts within the work setting have increased by 63% in the last two weeks whereas contacts within the home and other setting (contacts outside home, school and work) have remained at a similar level.
  • Mean contacts have increased in the 18-29 and 30-39 age groups by approximately 29% and 20% respectively. Increases across the age groups are largely driven by a rise in contacts within the work setting.
  • The highest interactions between age groups is between those 30-39 with those under 18. The biggest increase in interactions in the last two weeks is seen between those within 18-49 age groups with individuals aged between 5-12.
  • The proportion of individuals using public transport has decreased from approximately 25% to 21% with individuals visiting a pub or restaurant also decreasing, from 49% to 46%, in the last two weeks.
  • The proportion of individuals wearing a face covering where they have at least one contact outside of the home has decreased slightly compared to two weeks prior, from 84% to 81%.
  • Hospitalisations are rising. Future hospital occupancy and intensive care use are likely to continue rising.
  • Modelled rates of positive tests per 100K using data to 3rd September indicate that, for the week commencing 19th September 2021, there are 29 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability.
  • Of these, 18 local authorities are expected to exceed 500 cases per 100k with at least 75% probability. These are Aberdeen City, Aberdeenshire, City of Edinburgh, Dundee City, East Ayrshire, East Dunbartonshire, East Renfrewshire, Falkirk, Fife, Glasgow City, Highland, North Ayrshire, North Lanarkshire, Renfrewshire, South Ayrshire, South Lanarkshire, West Dunbartonshire and West Lothian.
  • Four local authorities (Fife, Glasgow City, North Lanarkshire and Renfrewshire) are expected to exceed 1000 cases per 100k with at least 75% probability.
  • Nationwide, levels of Covid-19 in wastewater have risen by around 64% since the previous week. In the week prior, levels increased by 30%.
  • As a result Covid-19 levels in wastewater this week are at the highest reported since the start of the pandemic.
  • Modelling of Long Covid estimates that on 26th 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 unchanged 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 8th September 2021

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 24th August (dashed line 1). This report covers the period up to 3rd September 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 6th 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 24th August[1] in Scotland was between 1.2 and 1.5 (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.

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 24th August, including 90% confidence intervals, produced by EMRG [3].

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 24th August, was that the incidence of new daily infections in Scotland was between 118 and 214 new infections per 100,000. This equates to between 6,400 and 11,700 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as at 24th August, including 90% confidence intervals, produced by EMRG 2.

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 7% per day as at 24th August. The lower and upper limits have decreased since last week.

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

Average contacts have increased by approximately 14% in the last two weeks (comparing surveys pertaining to 19th August - 25th August and 2nd September - 8th September) with a current level of 5.3 daily contacts as seen in Figure 4. Mean contacts within the work setting (Figure 5) have increased by 63% in the last two weeks whereas contacts within the home and other setting (contacts outside home, school and work) have remained at a similar level.

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. Mean contacts have increased in the 18-29 and 30-39 age groups by approximately 29% and 20% respectively. 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).

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 19th August - 25th August and 2nd September - 8th September and the difference between these periods. The highest interactions between age groups is between those 30-39 with those under 18. The biggest increase in interactions in the last two weeks is seen between those within 18-49 age groups with individuals aged between 5-12.

Figure 6. Overall mean contacts by age group for the weeks relating to 19th August - 25th August and 2nd September - 8th September.

Heat maps showing the mean contacts by age group in the weeks of 19th August and 2nd September.

As seen in Figure 7, the proportion of participants visiting different locations remains at similar levels across the majority of locations. The biggest changes are seenwith those using public transport and also individuals visiting a pub or restaurant. The proportion of individuals using public transport decreased from approximately 25% to 21% with individuals visiting a pub or restaurant also decreasing, from 49% to 46%, in the last two weeks.

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.

Figure 8 shows the number of people wearing a face covering where they have at least one contact outside of the home. This has decreased slightly compared to two weeks prior, from 84% to 81%.

Figure 8. 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)

From Figure 9, it can be seen that the older age groups have lower levels of contacts and 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 A, weekly cases, covid-19 hospital admissions and deaths [4] and cumulative vaccinations by age band [5].

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 26th September.

Worse assumes that infections have followed waste water data and continued to rise over the past week, in spite of the plateau in cases confirmed by PCR. Central follows recent confirmed case trends, and accounts for the possibility of an increase in the next few weeks as universities return. Better assumes that transmission will fall from the current level[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 6th September.

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 6th September.

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 6th September.

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 6th September 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 6th September. 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 28th 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.

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.

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 6th September 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 3rd September (Figure 15) indicate that, for the week commencing 19th September 2021, there are 29 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability[10].

Of these, 18 local authorities are expected to exceed 500 cases per 100k with at least 75% probability. These are Aberdeen City, Aberdeenshire, City of Edinburgh, Dundee City, East Ayrshire, East Dunbartonshire, East Renfrewshire, Falkirk, Fife, Glasgow City, Highland, North Ayrshire, North Lanarkshire, Renfrewshire, South Ayrshire, South Lanarkshire, West Dunbartonshire and West Lothian.

Four local authorities (Fife, Glasgow City, North Lanarkshire and Renfrewshire) 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 (19th to 25th September 2021), data to 3rd September.

A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (19th to 25th 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 Covid-19 have continued to rise to around 180 million gene copies per person per day (Mgc/p/d) compared to around 110 million gene copies per person per day (Mgc/p/d) last week, increasing by approximately 64%. This means wastewater virus levels are currently at the highest levels since the wider monitoring scheme started in August 2020.

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. Although both wastewater and new cases have risen in the last week, the smoothed 7 day running mean of national average new case rates suggests that the number of new cases may have stabilised in the last few days. This is not reflected in the national level wastewater data shown in Figure 16.

Figure 16. National average trends in wastewater and daily new case rates (7 day moving average). Anomalously high values, one in Seafield (Edinburgh) in mid-February (see Issue 40), one in Dunblane in mid-June, and two in Daldowie in January, were removed.

A line chart showing national average trends in wastewater Covid-19 and daily case rates.

At some sites, such as Seafield in Edinburgh (Figure 17), the levels of wastewater Covid-19 appear to have stopped rising in the last week, while at other sites such as Hatton (Figure 18), which covers Dundee City, levels have continued to rise.

Figure 17. Wastewater Covid-19 and daily case rate (7 day moving average) for Seafield in City of Edinburgh (covered pop: 606k). The black line and red shaded area provide a smoothed curve and confidence interval for wastewater Covid-19 that is estimated from a generalised additive model based on a Tweedie distribution.

A line chart showing average trends in wastewater Covid-19 and daily case rates for Seafield in Edinburgh.

Figure 18. Wastewater Covid-19 and daily case rate (7 day moving average) for Hatton in Dundee City (covered pop: 194k). The black line and red shaded area provide a smoothed curve and confidence interval for wastewater Covid-19 that is estimated from a generalised additive model based on a Tweedie distribution.

A line chart showing average trends in wastewater Covid-19 and daily case rates for Hatton in Dundee.

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 26th September 2021 between 45,000 (0.8% of the population) and 121,000 (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 26th 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