Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 70)

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. 70)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 70)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 70)

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 16th 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 0.8 and 1.1, with the growth rate between -3% and 2%.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.8 and 1.1, as of 7th September. The lower and upper limits have decreased since last week.
  • The number of new daily infections for Scotland is estimated as being between 219 and 394, per 100,000 people. The lower and upper limits have increased since last week.
  • The growth rate for Scotland is currently estimated as between -3% and 2%. The lower and upper limits have decreased since last week. While the R number and growth rate have decreased this week, they have been consistently above 1 and 0% respectively for several weeks previously, indicating a growing epidemic, corresponding to an increasing incidence.
  • Average contacts have decreased by 6% in the last two weeks (comparing surveys pertaining to 2nd September - 8th September and 16th September - 22nd September) with a current level of 5 daily contacts.
  • Mean contacts within the work have decreased by approximately 17% whereas contacts in the other setting (contacts outside home, school and work) have increased by 6% in the last two weeks. Contacts within the home have remained at a similar level over the same period.
  • Although overall adult contacts have decreased, mean contacts for those within the 18-28 age group and individuals 60 and over have increased contacts within the last two weeks, all other age groups have reported a decrease by at least 17%. Increases in contacts are largely driven by contacts within the other setting (contacts outside home, school and work).
  • Those aged between 18-59 have reported a decrease in interactions with those aged under 18. The biggest increase in interactions in the last two weeks is seen between those within 18-29 with each other, rising by around 50%.
  • The proportion of individuals visiting a pub or restaurant increased from approximately 46% to 49% with individuals visiting a healthcare facility decreasing from 20% to 17% in the last two weeks.
  • The proportion of contacts reported to have been indoors only has increased from 55% to 61% within the last two weeks whereas the proportion of contacts occurring outside only has shown a decrease over the same period.
  • The number of people wearing a face covering where they have at least one contact outside of the home has remained at a similar level, currently at 82%.
  • Hospital and ICU occupancies have plateaued. The scale of any future increase or decrease in hospital occupancy and intensive care use is highly uncertain, and depends on the number of infections.
  • Modelled rates of positive tests per 100K using data to 20th September indicate that, for the week commencing 3rd October 2021, there are 29 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability.
  • Of these, 2 local authorities are expected to exceed 300 cases per 100k with at least 75% probability. These are South Ayrshire and Stirling.
  • There are no local authorities which are expected to exceed 500 cases per 100k with at least 75% probability.
  • Nationwide, levels of Covid-19 in wastewater have declined since the previous week.
  • Modelling of Long Covid gives estimates that on 10th October 2021 between 1.0% and 2.2% of the population are projected to experience symptoms for 12 weeks or more after their first suspected Covid infection in Scotland. The upper limit is unchanged from last week.

Recent cases

Figure 1 shows the number of cases reported in Scotland between July and September 2021[1]. 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 22nd September 2021
A chart showing the number of cases reported in Scotland between July and September, and the cut off points for each of the modelling inputs.

R, growth rate and incidence are as of 7th September (dashed line 1). The medium term projections by the Scottish Government of infections, hospitalisations and ICU beds, the modelled rates of positive tests per 100k, the wastewater analysis and the long Covid analysis use data to 20th September (dashed line 2). Contact pattern data is to 22nd 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 7th September[2] in Scotland was between 0.8 and 1.1 (see Figure 2)[3].

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 7 th September, including 90% confidence intervals, produced by EMRG [4].
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 7th September, was that the incidence of new daily infections in Scotland was between 219 and 394 new infections per 100,000. This equates to between 12,000 and 21,500 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as at 7 th September, 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 2% per day as at 7th September. The lower and upper limits have decreased since last week.

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

Average contacts have decreased by 6% in the last two weeks (comparing surveys pertaining to 2nd September - 8th September and 16th September - 22nd September) with a current level of 5 daily contacts as seen in Figure 4. Mean contacts within the work have decreased by approximately 17% whereas contacts in the other setting (contacts outside home, school and work) have increased by 6% in the last two weeks. Contacts within the home have remained at a similar level over the same period.

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

Figure 5 shows how contacts change across age group and setting. Although overall adult contacts have decreased, mean contacts for those within the 18-28 age group and individuals 60 and over have increased contacts within the last two weeks, all other age groups have reported a decrease by at least 17%. Increases in contacts are largely driven by contacts within the other setting (contacts outside home, school and work).

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 2nd September - 8th September and 16th September - 22nd September and the difference between these periods. Those aged between 18-59 have reported a decrease in interactions with those aged under 18. The biggest increase in interactions in the last two weeks is seen between those within 18-29 with each other, rising by around 50%.

Figure 6: Overall mean contacts by age group for the weeks relating to 2nd September - 8th September and 16 th September - 22 nd September.
Heat maps showing the mean contacts by age group in the weeks of 2nd September and 16th 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 seen with those using visiting a pub or restaurant and also individuals visiting a healthcare facility. The proportion of individuals visiting a pub or restaurant increased from approximately 46% to 49% with individuals visiting a healthcare facility decreasing from 20% to 17% 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 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 from 55% to 61% 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.
A line chart showing the proportion of participants reported indoors and outdoors for contacts individually reported for Panel A.

Figure 9 shows the number of people wearing a face covering where they have at least one contact outside of the home. This has remained at a similar level, currently at 82%.

Figure 9: 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 10, it can be seen that the oldest age group has lower levels of contacts and higher vaccinations than the youngest age groups, 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 10: Average contacts for Panel A, weekly cases, covid-19 hospital admissions and deaths [5] and cumulative vaccinations by age band [6]
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 11 shows two projections over the three weeks to 10th October.

‘Central’ assumes that infections have plateaued. ‘Better’ assumes that infections continue to fall[7].

Figure 11. 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 20th 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 12 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 plateaued. The scale of any future increase or decrease in hospital occupancy and intensive care use is highly uncertain, and depends on the number of infections.

Figure 12. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 20th September.
A line graph showing the short term forecast of hospital bed demand.

Figure 13 shows the impact of the projection on ICU bed demand.

Figure 13. Medium term projections of modelled ICU bed demand, from Scottish Government modelling [9], based on positive test data reported up to 20th 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[10] (Figures 14 and 15), combining estimates from several independent models (including the Scottish Government’s logistics modelling, as shown in Figures 11-13). 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 20th 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 20th 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 5th October, 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 14. 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 15. 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 20th 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 UKHSA 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 20th September (Figure 16) indicate that, for the week commencing 3rd October 2021, there are 29 local authorities which are expected to exceed 50 cases per 100k with at least 75% probability[11].

Of these, 2 local authorities are expected to exceed 300 cases per 100k with at least 75% probability. These are South Ayrshire and Stirling.

There are no local authorities which are expected to exceed 500 cases per 100k with at least 75% probability[12].

Figure 16. Probability of local authority areas exceeding thresholds of cases per 100K (3rd to 10th October 2021), data to 20th September [13].
A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (3rd October to 10th October 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 RNA have fallen to around 100 Mgc/p/d from between 250 and 300 Mgc/p/d two weeks ago (depending on whether or not potentially anomalous values were excluded). This corresponds to the recent fall in the number of new cases.

Figure 17 shows the national running average trend for the full set of sampled sites. Note that in this report a new methodology for visualization of national trends has been introduced (see methodology update).

Figure 17. National running average trends in wastewater Covid 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. For this graph, a wastewater Covid average using the last 7 days of data is computed at every sampling date.
A line chart showing national average trends in wastewater Covid-19 and daily case rates.

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 self-reported 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 10th October 2021 between 54,000 (1.0% of the population) and 120,000 (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 18. Estimates of long Covid prevalence at 12 weeks from 16 th February 2020 to 10 th October 2021 for the better long Covid rates (showing 90% confidence interval). 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