Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no.77)

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.77)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 77)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 77)

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 4th 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 0.9 and 1.1, with the growth rate between -2% and 1%.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.9 and 1.1, as of 26th October. This has not changed since last week.
  • The number of new daily infections for Scotland is estimated as being between 70 and 117, per 100,000 people.
  • The growth rate for Scotland is currently estimated as between -2% and 1%. The lower limit has increased since last week.
  • Average contacts have increased by 8% in the last two weeks (comparing surveys pertaining to 14th October - 20th October and 28th October - 3rd November) with a current level of 5 daily contacts.
  • Mean contacts within the work setting have increased by 44% in the last two weeks. Contacts within the home and other setting (contacts outside home, school and work) have remained at a similar level over the same period.
  • Those aged between 50-59 reported the biggest increase in overall contacts, increasing by approximately 40% in the last week. This increase is largely driven by a rise in contacts within the other setting.
  • In the last two weeks, those aged between 30-39 have reported the biggest increase in interactions with individuals aged under 18. The 18-29 age groups have reported the biggest decrease in interactions with each other over the same period.
  • The biggest changes in the proportion of participants visiting different locations is seen in those attending an event outside and those visiting a pub or restaurant. Visits to an outdoor event have decreased from approximately 72% to 68% with individuals attending an pub or restaurant decreasing from 52% 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 71%.
  • The number of people wearing a face covering where they have at least one contact outside of the home remains at a similar level to two weeks prior, currently at 80%.
  • 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 8th November indicate that, for the week commencing 21st November 2021, 30 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. The only exceptions to this are the Orkney Islands and Shetland Islands.
  • 27 local authorities are expected to exceed 100 cases per 100K with at least 75% probability. The exceptions are Edinburgh, Glasgow, Na h‑Eileanan Siar, Orkney Islands and Shetland Islands.
  • There are no local authorities which are expected to exceed 300 cases per 100K with at least 75% probability.
  • Nationwide, wastewater Covid-19 levels have dropped by 7% compared to last week, but is still higher than it was a fortnight ago.
  • Modelling of long Covid estimates that on 28th 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 infection in Scotland. The lower and upper limits of the estimate are unchanged from 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 11th November 2021 [1]
Figure 1. A chart showing the number of cases reported in Scotland between May and October, and the cut off points for each of the modelling inputs.

R, growth rate and incidence are as of 26th October (dashed line 1). The Scottish Contact Survey uses data to 3rd November (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 8th November (dashed line 3). Wastewater analysis uses data to 9th 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 26th 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 26th October, including 90% confidence intervals, produced by EMRG [4].
Figure 2. A graph showing the range of values which each of the academic groups reporting an R value to SAGE are likely to lie within.

Source: EMRG

The various groups which report to the EMRG use different sources of data in their models to produce estimates of incidence (Figure 3). UKHSA's consensus view across these methods, as at 26th October, was that the incidence of new daily infections in Scotland was between 70 and 117 new infections per 100,000. This equates to between 3,800 and 6,400 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as at 26th October, including 90% confidence intervals, produced by EMRG 4.
Figure 3. A graph showing the ranges the values which each of the academic groups in SPI-M are reporting for incidence (new daily infections per 100,000) are likely to lie within.

Source: EMRG

The consensus from UKHSA for this week is that the growth rate in Scotland is between -2% and 1% per day as at 26th October. The lower limit has increased since last week.

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

Average contacts have increased by 8% in the last two weeks (comparing surveys pertaining to 14th October - 20th October and 28th October - 3rd November) with a current level of 5 daily contacts as seen in Figure 4. Mean contacts within the work setting have increased by 44% in the last two weeks. Contacts within the home and other setting (contacts outside home, school and work) have remained at a similar level over the same period.

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

Figure 5 shows how contacts change across age group and setting. Those aged between 50-59 reported the biggest increase in overall contacts, increasing by approximately 40% in the last week. This increase is largely driven by a rise 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).
Figure 5. A series of line graphs showing mean adult contacts by setting and age group for panel A and panel B from December 2020 to November 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 14th October - 20th October and 28th October - 3rd November and the difference between these periods. In the last two weeks, those aged between 30-39 have reported the biggest increase in interactions with individuals aged under 18. The 18‑29 age groups have reported the biggest decrease in interactions with each other over the same period.

Figure 6: Overall mean contacts by age group before for the weeks 14th October - 20th October and 28th October - 3rd November.
Figure 6. Heat maps showing the mean contacts by age group in the weeks of 14 October and 28 October.

As shown in Figure 7, the biggest changes in the proportion of participants visiting different locations is seen in those attending an event outside and those visiting a pub or restaurant. Visits to an outdoor event have decreased from approximately 72% to 68% with individuals attending an pub or restaurant decreasing from 52% to 48% in the last two weeks.

Figure 7: Locations visited by participants at least once for panel A and B (from SCS).
Figure 7. A series of line graphs showing locations visited by participants at least once for panel A and B in various settings.

Figure 8 shows the proportion of participants that reported contacts had indoors and outdoors for contacts individually reported for panel A. 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 71%.

Figure 8: Proportion of participants reported indoors and outdoors for contacts individually reported for panel A.
Figure 8. A line graph showing proportion of participants reported indoors and outdoors for contacts individually reported for panel B.

Figure 9 shows the number of people wearing a face covering where they have at least one contact outside of the home. This remains at a similar level to two weeks prior, currently at 80%.

Figure 9: Proportion of adults wearing a face coverings over time (with at least one contact outside of the home).
Figure 9. 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 28th 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[5]. 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.

Figure 10. Medium term projections of modelled total new daily infections, adjusting positive tests [6] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 8th November.
Figure 10. 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 8th November.
Figure 11. A line graph showing the short term forecast of hospital bed demand.

Figure 12 shows the impact of the projection on ICU bed demand.

Figure 12. Medium term projections of modelled ICU bed demand, from Scottish Government modelling [7], based on positive test data reported up to 8th November.
Figure 12. A line graph showing a short term forecast of modelled ICU bed demand.

A comparison of the actual data against historical projections is included in the Technical Annex.

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

SPI-M produces projections of the epidemic[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 8th 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 8th 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 7th 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.

Figure 13. SPI-M medium-term projection of daily hospitalisations in Scotland, at 50% and 90% credible intervals.
Figure 13. A combination scatter and line chart, showing the SAGE medium term projection of hospitalisations against the actual hospitalisations.
Figure 14. SPI-M medium-term projection of daily deaths in Scotland, at 50% and 90% credible intervals.
Figure 14. 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 8th 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, particularly in regions which have seen a new recent growth in cases.

Modelled rates of positive tests per 100K using data to 8th November (Figure 15) indicate that, for the week commencing 21st November 2021, 30 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. The only exceptions to this are the Orkney Islands and Shetland Islands.

27 local authorities are expected to exceed 100 cases per 100K with at least 75% probability. The exceptions are Edinburgh, Glasgow, Na h‑Eileanan Siar, Orkney Islands and Shetland Islands.

There are no local authorities which are expected to exceed 300 cases per 100K with at least 75% probability[9].

Figure 15. Probability of local authority areas exceeding thresholds of cases per 100K (21st to 27th November 2021), data to 8th November.
Figure 15. A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K.

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

Levels of Covid-19 in 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 dropped by 7% compared to last week, but is still higher than it was a fortnight ago. The week ending on the 9th of November saw a level of around 62 million gene copies per person per day (Mgc/p/d), down from 66 Mgc/p/d in the previous week (27/10/21 to 2/11/21). WW viral RNA levels continue to fluctuate significantly, but in terms of overall trends in the last month, appear to be fairly flat. This is similar to results in the ONS Coronavirus Infection Survey and PHS's rate of new cases.

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. This also shows overlaid data from the latest ONS Coronavirus Infection Survey (CIS) which gives estimates of the percentage of the Scottish population testing positive up to 30th October. The scaling is chosen such that the recent peak percentages of COVID-19 positivity are approximately aligned with the peaks in new case rates. In this figure, average levels of WW COVID-19 RNA rose and rapidly fell over the last two weeks, ultimately leading to levels remaining approximately flat over the recent period. The CIS positivity estimate also rose and fell, albeit to a lesser degree (and within the confidence interval on the estimation) and with a slightly different timing.

Figure 16. National running average trends in wastewater Covid-19, daily new case rates (7 day moving average) as of 9th November. Anomalously high values, one in Seafield (Edinburgh) in mid-February (see Issue 40), and the ONS Coronavirus Infection Survey ( CIS) positivity percentage [10].
Figure 16. 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 17.

This modelling estimates that at 28th November 2021 between 75,000 (1.4% of the population) and 158,000 (2.9%) 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 unchanged since last week.

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

Figure 17. Estimates of self-classified long Covid prevalence at 12 weeks from 16th February 2020 to 28th November 2021 (showing 90% confidence interval). ONS estimates of self-reported long Covid with range also shown.
Figure 17. A line 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