Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 80)

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. 80)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 80)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 80)

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 25th November 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%.

It is too soon to take account of the potential impact of Omicron within the modelling presented in this report. Therefore projections included are based on Delta only. In the coming weeks we hope to have further data to enable us to model the impact of Omicron with some degree of confidence.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.8 and 1.1, as of 16th November. The lower estimate has decreased since last week.
  • The number of new daily infections for Scotland is estimated as being between 79 and 121 as at 16th November, per 100,000 people.
  • The growth rate for Scotland is currently estimated as between -3% and 1%. The lower limit has decreased since last week.
  • Average contacts from the most recent Panel B cohort of the Scottish Contact Survey (week ending 24th November) indicate an average of 5.2 contacts.
  • Mean contacts within the other setting (contacts outside home, school and work) have decreased by 11% in the last two weeks. Contacts within the home and work setting remained at a similar level over the same period.
  • Differences across age groups are largely driven by changes in contacts within the workplace. Those aged between 18-49 have all reported an increase in contacts within the last two weeks, rising by at least 12%. Individuals aged between 50-69 decreased their overall contacts by at least 14%.
  • Those aged between 30-39 have reported the biggest increase in interactions with those aged under 18 in the last two weeks.
  • The biggest change in the proportion of participants visiting different locations, though slight, is seen in those visiting an non-essential shop, increasing from 42% to 44% in the last two weeks.
  • The number of people wearing a face covering where they have at least one contact outside of the home has decreased in the last two weeks from 83% to 81%.
  • The recent fall in hospital occupancy may have levelled off. ICU occupancy has fallen slightly. 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 29th November indicate that, for the week commencing 12th December 2021, 29 of the 32 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. These 29 local authorities are also expected to exceed 100 cases per 100K with at least 75% probability.
  • There are no local authorities which are expected to exceed 300 cases per 100K with at least 75% probability.
  • Nationwide, Covid-19 wastewater levels have continued to increase, with the week ending on 25th November seeing levels of around 80 million gene copies per person per day (Mgc/p/d), up from around 70 Mgc/p/d in the previous week.
  • Modelling of long Covid estimates that on 19th December 2021 between 1.5% and 3.1% of the population are projected to self-classify with long Covid for 12 weeks or more after their first suspected Covid infection in Scotland. The lower and upper limits of the estimate are higher than last week.

Recent cases

Figure 1 shows the number of Covid-19 cases reported in Scotland between November and December 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 2nd December 2021
A chart showing the number of cases reported in Scotland between November and December 2021, and the cut off points for each of the modelling inputs.

R, growth rate and incidence are as of 16th November (dashed line 1). The Scottish Contact Survey uses data to 24th November (dashed line 2). Wastewater analysis used data to 25th November (dashed line 3).

The Scottish Government modelling of infections, hospitalisations and ICU beds, the long Covid analysis, the medium term projections and the modelled rates of positive tests per 100K use data to 29th 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 16th November[1] in Scotland was between 0.8 and 1.1 (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 16th November, 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 16th November, was that the incidence of new daily infections in Scotland was between 79 and 121 new infections per 100,000. This equates to between 4,300 and 6,600 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as at 16th November, including 90% confidence intervals, produced by EMRG 4.
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 as at 16th November. The lower limit has decreased since last week.

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

Average contacts from the most recent Panel B cohort of the Scottish Contact Survey (week ending 24th November) indicate an average of 5.2 contacts. This has remained at similar levels compared to the previous Panel B of the survey (week ending 10th November), as seen in Figure 4.

Mean contacts within the other setting (contacts outside home, school and work) have decreased by 11% in the last two weeks. Contacts within the home and work setting 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. Differences across age groups are largely driven by changes in contacts within the workplace. Those aged between 18-49 have all reported an increase in contacts within the last two weeks, rising by at least 12%. Individuals aged between 50-69 decreased their overall contacts by at least 14%.

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 November 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 4th November - 10th November and 18th November - 24th November, and the difference between these periods. Those aged between 30-39 have reported the biggest increase in interactions with those aged under 18 in the last two weeks.

Figure 6: Overall mean contacts by age group before for the weeks relating to 4th November - 10th November and 18th November -24th November.
Heat maps showing the mean contacts by age group in the weeks beginning 4th November and 18th November.

As shown in Figure 7, the biggest change in the proportion of participants visiting different locations, though slight, is seen in those visiting an non-essential shop, increasing from 42% to 44% 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 difference in contacts between those who work from home compared to those who have a workplace outside of the home. This shows that those who do not work from home have higher and more variable contacts than those who work from home. This also shows that contacts had within the work place make up the majority of overall contacts for those who do not work at home, therefore changes in work contacts has proportionate impact on overall contacts.

Figure 8: Overall mean contacts by work location (home or away from home) for each panel for adults in Scotland, truncated to 100 contacts per participant (from SCS).
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 decreased in the last two weeks from 83% to 81%.

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 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 20th December.

‘Central’ assumes that infections will fall. ‘Worse’ assumes a rise in transmission from the current level. ‘Better’ assumes a larger drop in transmission[4]. As it is too soon to take account of the potential impact of the Omicron variant, all three scenarios are based on the Delta variant. Therefore dependingon the current number of Omicron cases and its characteristics, the actual number of infections, hospital occupancy and ICU occupancy over the next few weeks could be higher than projected here.

Figure 10. Medium term projections of modelled total new daily infections, adjusting positive tests [5] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 29th November [6].
A line graph showing the short term forecast of modelled new infections.

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.

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

Figure 11. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 29th November.
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 [7], based on positive test data reported up to 29th November.
A line graph showing a short term forecast of modelled ICU bed demand.

The methodology for estimating projections is included in the Technical Annex. Also included is a comparison of the actual data against historical projections.

What the modelling tells us about projections of hospitalisations and deaths in the medium term

SPI-M produces projections of the epidemic[8] (Figures 13 and 14), combining estimates from several independent models (including the Scottish Government’s logistics modelling, as shown in Figures 10 to 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 22nd November and do not include the effects of any future increase in the Omicron variant, or 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 22nd 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 21st December.

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.

These projections do not consider the potential impact of the Omicron variant.

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, at 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 29th 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.

There is uncertainty in regions with smaller populations, and hence lower test counts, in particular in regions such as Na h-Eileanan Siar, Orkney Islands and Shetland Islands.

Modelled rates of positive tests per 100K using data to 29th November (Figure 15) indicate that, for the week commencing 12th December 2021, 29 of the 32 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. These 29 local authorities are also expected to exceed 100 cases per 100K with this probability[9].

There are no local authorities which are expected to exceed 300 cases per 100K with at least 75% probability[10].

These models are based on the Delta variant only.

Figure 15. Probability of local authority areas exceeding thresholds of cases per 100K (12th to 18th December 2021), data to 29th November.
A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (12th December to 18th December 2021).

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

Levels of Covid-19 RNA in wastewater (WW) collected at a number of sites around Scotland are adjusted for population and local changes in intake flow rate (or ammonia levels where flow is not available) 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 Covid-19 levels have continued to increase, with the week ending on 25th November seeing levels of around 80 million gene copies per person per day (Mgc/p/d), up from around 70 Mgc/p/d in the previous week (week ending 18th November). This creates an apparent discrepancy with case rates, which have decreased slightly in recent times, but does match an increase seen in the Office of National Statistics’ Coronavirus Infection Survey.

Figure 16 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 appear to have increased (though to a lesser extent than last week) across most of Scotland but this change is not as yet reflected in the case rate, which has shown a continued decrease during the past week across much of Scotland. Due to periods of public holiday the last samples obtained for the WW analysis have been from 25th November, and thus the data are slightly outdated this week. Further, unforeseen building closure at SEPA’s facilities has meant that no further samples could be processed this week. However, the week’s sampling total stands at 205 samples, an improvement from last week.

In Figure 16 we also show data from the Office of National Statistics’ Coronavirus Infection Survey, with positivity estimates up to 20th November. In contrast to reported case rates, this survey data shows an increase of Covid-19 prevalence in line with wastewater Covid-19 levels, although further monitoring of both wastewater and ONS data is required to fully assess this apparent alignment.

Figure 16. National running average trends in wastewater Covid-19 and daily new case rates (7-day moving average) up until 25th November [11].
A line chart showing national average trends in wastewater Covid-19 and daily case rates.

One example of the recent discrepancy between WW and new case rates is at Nigg, which covers nearly 80% of Aberdeen City (Figure 17). A similar trend in relationship is observed in other areas, for example, NHS Lothian.

Figure 17. Wastewater Covid-19 and daily case rate (7 day moving average) for Nigg, covering most of Aberdeen (covered pop: 218k) [12].
A line chart showing national average trends in wastewater Covid-19 and daily case rates for Nigg in Aberdeen.

Figures 18 and 19 present respective trends seen in NHS Greater Glasgow & Clyde, and NHS Lanarkshire, which have seen small numbers of reported cases of the new Covid-19 Omicron variant. In both health boards a similar discrepancy can be observed between wastewater and case rates, as seen on the national level. Indeed the rise in WW viral levels in these health boards is very close to the national average.

Figure 18. Average trends in wastewater Covid-19 and daily case rates (7 day moving average) in NHS Greater Glasgow and Clyde (pop: 1147k)
A line chart showing national average trends in wastewater Covid-19 and daily case rates for NHS Greater Glasgow and Clyde.
Figure 19. Average trends in wastewater Covid-19 and daily case rates (7 day moving average) in NHS Lanarkshire (pop: 668k)
A line chart showing national average trends in wastewater Covid-19 and daily case rates for NHS Lanarkshire.

This week’s data has shown a noticeable decrease from a previous peak in Kirkwall’s WW viral levels and case rates. Meanwhile, Lerwick in the Shetland Islands (covered population 8k) has shown a large increase in WW viral levels to match a recent increase in case rates, though the most recent data shows that case rates have since considerably decreased.

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 20.

This modelling estimates that at 19th December 2021 between 80,000 (1.5% of the population) and 169,000 (3.1%) people are projected to self-classify with long Covid for 12 weeks or more after their first suspected Covid infection in Scotland. The lower and upper 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 20. Estimates of self-classified long Covid prevalence at 12 weeks from 16th February 2020 to 19th December 2021 (showing 90% confidence interval). ONS estimates also shown [13].
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.

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