Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no.78)

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.78)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 78)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 78)

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 11th 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 2%.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.9 and 1.1, as of 2nd November. This has not changed since last week.
  • The number of new daily infections for Scotland is estimated as being between 86 and 112, per 100,000 people.
  • The growth rate for Scotland is currently estimated as between -2% and 2%. The upper limit has increased since last week.
  • Average contacts from surveys pertaining to 4th November - 10th November indicate a current level of 5.1 daily contacts.
  • Mean contacts within the work setting have almost doubled in the last two weeks while contacts within the home and other setting (contacts outside home, school and work) have remained at a similar level over the same period.
  • All age groups increased their mean contacts within the last two weeks. This was largely driven by a rise in contacts within the work place. The largest increase was reported by the 18-29 age group, increasing overall contacts by 44%.
  • Those aged between 18-29 have reported the biggest increase in interactions with those aged under 18 in the last two weeks.
  • The proportion of individuals visiting a healthcare facility increased from approximately 22% to 26% while individuals visiting a pub or restaurant decreased from 49% to 44% in the last two weeks.
  • The proportion of contacts reported to have been indoors only has remained at similar level to two weeks prior, currently at 69%.
  • 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 83%.
  • Modelled rates of positive tests per 100K using data to 15th November indicate that, for the week commencing 28th November 2021, all 29 local authorities included are expected to exceed 50 cases per 100K with at least 75% probability. All 29 are also expected to exceed 100 cases per 100K with this probability.
  • 10 local authorities are expected to exceed 300 cases per 100K with at least 75% probability. These are Angus, Clackmannanshire, Dumfries & Galloway, East Ayrshire, East Dunbartonshire, East Renfrewshire, Falkirk, Fife, South Ayrshire and South Lanarkshire.
  • There are no local authorities which are expected to exceed 500 cases per 100K with at least 75% probability.
  • Nationwide, wastewater (WW) Covid-19 levels have remained approximately flat over the recent two week period. The week ending on 15th November saw a level of around 55 million gene copies per person per day (Mgc/p/d), down from 57 Mgc/p/d in the previous week.
  • Modelling of long Covid estimates that on 5th December 2021 between 1.4% and 3.0% 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 upper limit of the estimate is higher than last week.

Recent cases

Figure 1 shows the number of Covid-19 cases reported in Scotland between October 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 18th November 2021

A chart showing the number of cases reported in Scotland between October and November 2021, and the cut off points for each of the modelling inputs.

R, growth rate and incidence are as of 2nd November (dashed line 1). The Scottish Contact Survey uses data to 10th November (dashed line 2). The Scottish Government modelling of infections, hospitalisations and ICU beds, the long Covid analysis, the medium term projections, the modelled rates of positive tests per 100K and the wastewater analysis use data to 15th November (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 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 2nd November[1] in Scotland was between 0.9 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 2nd 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 2nd November, was that the incidence of new daily infections in Scotland was between 86 and 112 new infections per 100,000. This equates to between 4,700 and 6,100 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as at 2nd 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 -2% and 2% per day as at 2nd November. The upper limit has increased 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 10th November) indicate an average of 5.1 contacts. Compared to the previous Panel B of the survey (week ending 27th October) this has increased by approximately 27% in the last two weeks, as seen in Figure 4.

Mean contacts within the work setting have almost doubled in the last two weeks while 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.

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. All age groups increased their mean contacts within the last two weeks. This was largely driven by a rise in contacts within the work place. The largest increase was reported by the 18-29 age group, increasing overall contacts by 44%.

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 21st October - 27th October and 4th November - 10th November, and the difference between these periods. Those aged between 18-29 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 21st October - 27th October and 4th November - 10th November.

Heat maps showing the mean contacts by age group in the weeks beginning 21st October and 4th November.

As shown in Figure 7, the biggest differences are seen with those visiting a healthcare facility and individuals visiting a pub or restaurant. The proportion of individuals visiting a healthcare facility increased from approximately 22% to 26% while individuals visiting a pub or restaurant decreased from 49% 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 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 remained at similar level to two weeks prior, currently at 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 remains at a similar level to two weeks prior, currently at 83%.

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 four weeks to 13th December.

'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[4].

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 15th 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 four weeks.

Figure 11. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 15th 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 15th November.

A line graph showing a short term forecast of modelled ICU bed demand.

A new 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 15th November 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 15th 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 14th 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.

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 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.

Due to inconsistent results from various models, UKHSA has not been able to provide estimates for the Orkney Islands, Shetland Islands or Na h-Eileanan Siar this week.

Modelled rates of positive tests per 100K using data to 15th November (Figure 15) indicate that, for the week commencing 28th November 2021, all 29 local authorities included are expected to exceed 50 cases per 100K with at least 75% probability. All 29 are also expected to exceed 100 cases per 100K with this probability.

10 local authorities are expected to exceed 300 cases per 100K with at least 75% probability. These are Angus, Clackmannanshire, Dumfries & Galloway, East Ayrshire, East Dunbartonshire, East Renfrewshire, Falkirk, Fife, South Ayrshire and South Lanarkshire.

There are no local authorities which are expected to exceed 500 cases per 100K with at least 75% probability[9].

Figure 15. Probability of local authority areas exceeding thresholds of cases per 100K (28th November to 4th December 2021), data to 15th November [10].

A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (28th November to 4th December 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 (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 (WW) Covid-19 levels have remained approximately flat over the recent two week period. The week ending on 15th November saw a level of around 55 million gene copies per person per day (Mgc/p/d), down from 57 Mgc/p/d in the previous week (week ending 8th November). These changes in WW Covid-19 levels are similar to recent trends in the ONS Coronavirus Infection Survey (CIS) and suggest the last month's Covid-19 measurements show fluctuating or uncertain levels around a high plateau.

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. In Figure 16 we also bring into consideration data from the ONS CIS up to 6th November, which has estimates of the percentage of the Scottish population testing positive. This is overlaid on the graph, with the scaling chosen such that the recent peak percentages of Covid-19 positivity are approximately aligned with the peaks in new case rates. In this figure, we see that average levels of WW Covid-19 have remained approximately flat over the recent two week period. The CIS positivity estimate are also approximately flat. Taken together with the constant rate of new cases, this suggests high and variable Covid-19 levels without a systematic trend upwards or downwards.

Figure 16. National running average trends in wastewater Covid-19 and daily new case rates (7 day moving average) up until 15th November [11].

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

Figure 17 uses colours to map (i) the local authority average WW viral Covid-19 levels (in Mgc/p/d) over the two-week period from 2nd November to 15th November, and (ii) the change in viral Covid-19 levels compared to the previous two-week period 19th October to 1st November. This shows that across large parts of the country, viral Covid-19 levels in wastewater have decreased since the observed peak at the end of October.

Figure 17. Map showing wastewater Covid-19 levels (million gene copies/person/day) for each local authority for 2nd November to 15th November and changes relative to 19th October to 1st November.

Two maps of Scotland, showing the wastewater levels for each local authority and the change relative to the previous period.

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 5th December 2021 between 78,000 (1.4% of the population) and 162,000 (3.0%) people are projected to self-classify with long Covid for 12 weeks or more after their first suspected Covid infection in Scotland. The upper limit of the estimate is 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 5th December 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