Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 76)

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. 76)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 76)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 76)

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 28th October 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 0.9 and 1.1, with the growth rate between -3% and 1%.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.9 and 1.1, as of 19th October. The lower and upper limits have increased since last week.
  • The number of new daily infections for Scotland is estimated as being between 63 and 96, per 100,000 people.
  • The growth rate for Scotland is currently estimated as between -3% and 1%. The upper limit has increased since last week.
  • Average contacts have decreased by 13% in the last two weeks (comparing surveys pertaining to 7th October - 13th October and 21st October - 27th October) with a current level of 4.1 daily contacts.
  • Mean contacts within the work and other setting (contacts outside home, school and work) have decreased in the last two weeks by 20% and 17% respectively. Contacts within the home have remained at a similar level over the same period.
  • Those aged between 30-39 and 50-59 reported an increase in overall contacts whereas all remaining age groups reported a decrease. Changes across the age groups are driven by contacts within the work place with the exception of the 18-29 age group, with their decrease driven by a reduction in contacts within the other setting.
  • Those aged between 18-29 have reported the biggest decrease in interactions with those aged under 18 in the last two weeks. The highest interactions remain between the 18-29 age group with each other.
  • The proportion of individuals using public transport increased from approximately 23% to 28% while individuals visiting another’s home rose from 44% to 48% in the last two weeks.
  • The proportion of contacts reported to have been indoors only has increased in the last two weeks from 66% to 69%.
  • The number of people wearing a face covering where they have at least one contact outside of the home has increased in the last two weeks from 80% to 84%.
  • New research from the EAVE II group indicates that for August to October 2021 most hospitalisations are among older double vaccinated individuals.
  • This study also shows that from August to October 2021 most hospitalisations are among double vaccinated individuals with multiple comorbid clinical conditions, though a substantial number are still unvaccinated individuals with no clinical conditions.
  • Hospital and ICU occupancies are in a plateau. There continues to be uncertainty over hospital occupancy and intensive care in the next three weeks.
  • Modelled rates of positive tests per 100K using data to 1st November indicate that, for the week commencing 14th November 2021, 31 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. The only exception to this is the Shetland Islands.
  • 29 local authorities are also expected to exceed 100 cases per 100K with at least 75% probability. The only exceptions are Na h-Eileanan Siar, Orkney Islands and Shetland Islands.
  • Clackmannanshire is the only local authority which is expected to exceed 300 cases per 100K with at least 75% probability.
  • Nationwide, Covid-19 levels in wastewater (WW) have shown an increase since last week (20th to 26th October), increasing by approximately 20%.
  • Modelling of long Covid estimates that on 21st November 2021 between 1.4% and 2.9% of the population are projected to self-classify with long Covid for 12 weeks or more after their first suspected Covid-19 infection in Scotland. The upper and lower limits of the estimate are higher than last week.

Recent cases

Figure 1 shows the number of Covid-19 cases reported in Scotland between July and November 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 4th November 2021 [1]
A chart showing the number of cases reported in Scotland between August and November 2021, and the cut off points for each of the modelling inputs.

R, growth rate and incidence are as of 19th October (dashed line 1). The Scottish Contact Survey uses data to 27th October (dashed line 2). The Scottish Government modelling of infections, hospitalisations and ICU beds, the long Covid analysis, the medium term projections and modelled rates of positive tests per 100K use data to 1st November (dashed line 3). Wastewater analysis uses data to 2nd November (dashed line 4).

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 and the UKHSA. 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 19th October[2] in Scotland was between 0.9 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 19th October, 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 19th October, was that the incidence of new daily infections in Scotland was between 63 and 96 new infections per 100,000. This equates to between 3,400 and 5,200 people becoming infected each day in Scotland. The lower and upper limits have decreased since last week.

Figure 3. Estimates of incidence for Scotland, as at 19th October, including 90% confidence intervals, produced by EMRG [4]. Source: EMRG
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.

The consensus from UKHSA for this week is that the growth rate in Scotland is between -3% and 1% per day as at 19th October. The upper limit has increased since last week.

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

Average contacts have decreased by 13% in the last two weeks (comparing surveys pertaining to 7th October - 13th October and 21st October - 27th October) with a current level of 4.1 daily contacts as seen in Figure 4. Mean contacts within the work and other setting (contacts outside home, school and work) have decreased in the last two weeks by 20% and 17% respectively. 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. Those aged between 30-39 and 50-59 reported an increase in overall contacts whereas all remaining age groups reported a decrease. Changes across the age groups are driven by contacts within the work place with the exception of the 18-29 age group, with their decrease driven by a reduction in contacts within the other 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 October 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 7th October - 13th October and 21st October - 27th October and the difference between these periods. Those aged between 18-29 have reported the biggest decrease in interactions with those aged under 18 in the last two weeks. The highest interactions remain between the 18-29 age group with each other.

Figure 6: Overall mean contacts by age group before for the weeks relating to 7th October - 13th October and 21st October - 27th October.
Heat maps showing the mean contacts by age group in the weeks beginning 7th October and 21st October.

As shown in Figure 7, the biggest differences are seen with those using public transport and also individuals visiting another’s home. The proportion of individuals using public transport increased from approximately 23% to 28% while individuals visiting another’s home rose from 44% to 48% 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 B. A contact can also be recorded as both indoor and outdoor. The proportion of contacts reported to have been indoors only has increased in the last two weeks from 66% to 69%.

Figure 8: Proportion of participants reported indoors and outdoors for contacts individually reported for panel B.
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 increased in the last two weeks to 84% from 80%.

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)

What we know about who is being admitted to hospital

The Early Pandemic Evaluation and Enhanced Surveillance of Covid-19 (EAVE 2) Study Group[5] has updated the pattern of demographics, deprivation, vaccine status and clinical risk groups over time for those who were admitted to hospital in Scotland (for further information see the Technical Annex in Issues 23 and 24 of these Research Findings). This update covers the demographics of emergency Covid-19 admissions to hospital in Scotland from 1st April 2021 to 25th October 2021.

As shown in Figure 10, in the earliest period (1st April to 31st July 2021) the majority of admissions to hospital following a positive Covid-19 test were among unvaccinated younger people, although a substantial number were elderly and double vaccinated. In the latest period (1st August to 25th October 2021) most hospitalisations are among older double vaccinated individuals. This may reflect a number of factors, e.g. waning vaccine protection, now that most of the adult population are now double vaccinated.

Figure 10. Number of Covid-19 admissions to hospital by age and vaccination status in two periods.
A series of bar charts showing hospital admissions by age and vaccination status, over two periods (April to July 2021 and August to October 2021)

Figure 11 shows the number of Covid-19 admissions to hospital by number of clinical risk groups and vaccination status. Risk group status is the number of Q-Covid[6] risk groups to which a person belongs. In the earliest period shown (1st April to 31st July 2021) the majority of hospitalisations following a positive Covid-19 test were among unvaccinated individuals, with no clinical risk groups. In the latest period (1st August to 25th October 2021) most hospitalisations are among double vaccinated individuals with multiple comorbid clinical conditions, though a substantial number are still unvaccinated individuals with no clinical conditions.

Figure 11. Number of Covid-19 admissions to hospital by number of clinical risk groups and vaccination status [7] in two periods.
A series of bar charts showing hospital admissions by clinical risk group and vaccination status, over two periods (April to July 2021 and August to October 2021)

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 21st November.

‘Central’ assumes that infections will rise or plateau at the current level, resulting from a small rise in transmission. ‘Worse’ assumes a larger rise in transmission from the current level. ‘Better’ assumes a small drop in transmission[8]. All three scenarios account for the end of the half-term periods and COP 26 in Glasgow. Due to this, there is a large amount of uncertainty as to the potential impact on infections.

Contacts tend to be lower during half term and holidays. The modelling accounts for a potential increase in transmission from schools reopening after half-term.

Figure 12. Medium term projections of modelled total new daily infections, adjusting positive tests [9] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 1st November.
A line graph showing the short term forecast of modelled new infections.

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.

There continues to be uncertainty over hospital occupancy and intensive care in the next three weeks.

Figure 13. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 1st November.
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 [10], based on positive test data reported up to 1st November.
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[11] (Figure 15), combining estimates from several independent models (including the Scottish Government’s logistics modelling, as shown in Figures 12 to 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 1st November and do not include the effects of any future policy or behavioural changes.

Due to an insufficient number of models, SPI-M has been unable to produce a consensus projection for deaths in Scotland this week. We hope to include a new set of projections in next week’s publication.

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 1st November. 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 should be used, with judgement, as the projection from which estimates may be derived until the 23rd November.

These projections include the potential impact of vaccinations over the next few weeks. Modelling groups have used their expert judgement and evidence from UKHSA, 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, at 50% and 90% credible intervals.
A combination scatter and line chart, showing the SAGE medium term projection of hospitalisations against the actual hospitalisations.

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 1st November 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.

This week, there remains increased uncertainty in estimates due to recent changes in case trends and the potential impact of half-term.

Modelled rates of positive tests per 100K using data to 1st November (Figure 16) indicate that, for the week commencing 14th November 2021, 31 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. The only exception to this is the Shetland Islands.

29 local authorities are also expected to exceed 100 cases per 100K with at least 75% probability. The only exceptions are Na h-Eileanan Siar, Orkney Islands and Shetland Islands.

Clackmannanshire is the only local authority which is expected to exceed 300 cases per 100K with at least 75% probability[12].

Figure 16. Probability of local authority areas exceeding thresholds of cases per 100K (14th to 20th November 2021), data to 1st November.
A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (14th to 20th November 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, wastewater (WW) Covid-19 levels have shown an initial increase followed by a downturn since last week (20th to 26th October), with a one-week average level ending on 2nd November of around 68 million gene copies per person per day (Mgc/p/d). This compares with 56 Mgc/p/d for the week ending 26th October, an increase of approximately 20%. Whilst the measured WW levels have fluctuated, case numbers remained steady at around 50 new cases per 100,000 population (7 day average), over the last month.

Figure 17 shows the national running average trend (over a 7-day period) for the full set of sampled sites, with a small number of unrealistically large outliers excluded. WW Covid-19 levels are still high, similar to those early in the year or shortly after the July peak.

Figure 17. National running average trends in wastewater Covid-19 and daily new case rates (7 day moving average) as of 2nd November [13]
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 gives a projection of estimated 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 21st November 2021 between 76,000 (1.4% of the population) and 159,000 (2.9%) people are projected to self-classify with long Covid for 12 weeks or more after their first suspected Covid-19 infection in Scotland. The upper and lower limits of the estimate are higher than 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 self-classified long Covid prevalence at 12 weeks from 16th February 2020 to 21st November 2021 (showing 90% confidence interval). ONS estimates of self-reported long Covid with range also shown.
A percentile chart showing the estimated number of long Covid prevalence at 12 weeks, compared to ONS estimates.

See the Technical Annex in issue 73 for information about the methodology.

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.

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