Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (Issue No. 63)

Published: 5 Aug 2021

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. 63)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 63)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 63)

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 30th July 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 0.7 and 0.9, with the growth rate between -5% and -2%, based on the period up to 2nd August.

The number of new cases in Scotland has been declining since the recent peak in early July (when there were over 400 per hundred thousand people). Last week the R number was below 1 for the first time since mid-May.

Hospital admissions have been declining slowly since mid-July and ICU admissions are now also beginning to decline. Acute bed occupancy has followed a similar trend, though ICU occupancy over the last few weeks is indicative of a plateau rather than a decline at this stage.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.7 and 0.9, based on the period up to 2nd August. The lower and upper limits have decreased since last week.
  • The number of new daily infections for Scotland is estimated as being between 58 and 114, per 100,000 people, based on the period up to 2nd August.
  • The growth rate for Scotland is currently estimated as between -5% and -2%, based on the period up to 2nd August.
  • Average contacts have remained at a similar level in the last two weeks (comparing surveys pertaining to 8th July - 14th July and 22nd July - 28th July) with a current level of 4.2 daily contacts.
  • Mean contacts for those aged between 40-49 and 60-69 have shown an increase in comparison to two weeks prior. For individuals aged between 40-49 this is largely driven by a rise in contacts within the work place in contrast to those aged 60-69 where this increase is driven by a rise in contacts within the home and other setting (contacts had outside of the work, school and home).
  • Interactions between those 18 and over with individuals under 18 have decreased in the last two weeks with the exception of those aged between 40-49 who have increased their interactions with this age group.
  • The proportion of participants visiting different locations remains at similar levels across the majority of locations with those visiting another's home reporting the highest increase from 47% to 53% in the last two weeks.
  • The proportion of contacts reported to have been indoors only has decreased within the last two weeks whereas the proportion of contacts occurring outside only has shown an increase over the same period.
  • Hospitalisations have been declining from a peak in mid-July. Potential future changes in hospital occupancy and intensive care use depends on both current infection levels and the impact of the recent and upcoming relaxations of measures which will take a few weeks to become apparent.
  • Modelled rates of positive tests per 100K using data to 2nd August indicate that, for the week commencing 15th August 2021, there are four local authorities with at least a 75% probability of exceeding 50 cases per 100k. These are Inverclyde, North Lanarkshire, South Lanarkshire and West Dunbartonshire. There are no local authorities which are expected to exceed 100 cases per 100k with at least a 75% probability.
  • Nationwide, relative to last week's reported levels, wastewater Covid‑19 RNA concentrations have fallen by around 20%. Compared to earlier in the year, the current levels of wastewater Covid are still in a similar range to late January/early February.
  • All sites, besides Edinburgh, show wastewater Covid-19 levels continuing to be higher than would be expected given the current rate of new cases.
  • The South Lanarkshire local authority overall wastewater Covid-19 level now is significantly above the national average, in contrast to the low levels of new cases observed.
  • The Scottish Government is modelling the number of people likely to experience long Covid symptoms. This modelling estimates that, on 22nd August 2021, between 0.7% and 1.9% of the population are projected to experience symptoms for 12 weeks or more after their first suspected Covid infection in Scotland.

Recent cases

Figure 1 shows the number of cases reported in Scotland between May and August 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 August 2021.

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

This report covers the period up to 28th July for contact patterns (indicated by dashed line 1). Wastewater data is provided to 30th July (dashed line 2). The estimates of R, incidence, growth rates, the modelled rates of positive tests per 100k, the medium term projections by the Scottish Government of infections, hospitalisations and ICU beds, and the long Covid analysis use data to 2nd August (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[1] 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.

What the modelling tells us about the epidemic as a whole

The R value and growth rates are estimated by several independent modelling groups based in universities, Public Health England (PHE) and the Joint Biosecurity Centre. Estimates are considered, discussed and combined at the Epidemiology Modelling Review Group (EMRG), which sits within the UKHSA.

R is an indicator that lags by two to three weeks and therefore does not reflect any behavioural changes that have happened during this time.

UKHSA's consensus view across these methods as of 4th August, using data to 2nd August, was that the value of R in Scotland was between 0.7 and 0.9 (see Figure 2)[2].

This week the Scottish Government presented two outputs to EMRG. The first uses confirmed cases as published by Public Health Scotland (PHS). The second uses instead wastewater data to estimate the number of cases. Both outputs are shown in Figures 2 and 3.

Figure 2. Estimates of R t for Scotland, as of 4th August, including 90% confidence intervals, produced by EMRG [3]. Data to 2 nd August.

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, using data to 2nd August, was that the incidence of new daily infections in Scotland was between 58 and 114 new infections per 100,000. This equates to between 3,200 and 6,200 people becoming infected each day in Scotland.

Figure 3. Estimates of incidence for Scotland, as of 4th August, including 90% confidence intervals, produced by EMRG 2. Data to 2nd August.

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 -5% and -2% per day using data to 2nd August. The lower and upper limits have decreased since last week.

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

Average contacts have remained at a similar level in the last two weeks (comparing surveys pertaining to 8th - 14th July and 22nd - 28th July) with a current level of 4.2 daily contacts as seen in Figure 4. Contacts across all settings have remained at similar levels compared to two weeks prior.

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. Mean contacts for those aged between 40-49 and 60-69 have shown an increase in comparison to two weeks prior. For individuals aged between 40-49 this is largely driven by a rise in contacts within the work place. For those aged 60-69 the increase is driven by a rise in contacts within the home and other setting (contacts had outside of the work, school and home).

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 July 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 8th July - 14th July and 22nd July - 28th July and the difference between these periods. Interactions between those 18 and over with individuals under 18 have decreased in the last two weeks with the exception of those aged between 40-49 who have increased their interactions with this age group.

Figure 6. Overall mean contacts by age group before the weeks relating to 8th July - 14th July and 22nd July - 28th July.

Heat maps showing the mean contacts by age group in the weeks of 8 July and 22 July.

As seen in Figure 7, the proportion of participants visiting different locations remains at similar levels across the majority of locations,with those visiting someone else's home reporting the highest increase from 47% to 53% in the last two weeks.

Figure 7. Locations visited by participants at least once for panel A and B (from SCS).

A series of line graphs showing locations visited by participants at least once for panel A and B in various settings.

Figure 8 shows the proportion of participants that reported contacts had indoors and outdoors for contacts individually reported for panel A. A contact can be recorded as both indoor and outdoor. The graph also shows contacts reported as outside only and indoor only. The proportion of contacts reported to have been indoors only has decreased within the last two weeks whereas the proportion of contacts occurring outside only has shown an increase over the same period.

Figure 8. Proportion of participants reported indoors and outdoors for contacts individually reported for panel A.

A line chart showing the proportion of contacts reported indoors, outdoors or both.

Vaccinations and contacts patterns

From Figure 9, it can be seen that the older age groups have fewer contacts and more vaccinations than the youngest age group, they also have the lowest weekly case number comparatively to the younger age groups. Despite that, they have similar, or higher for the oldest age group, weekly hospitalization levels and deaths to that seen with the younger age groups.

Figure 9: Average contacts for Panel A, weekly cases, covid-19 hospital admissions and deaths [4] and cumulative vaccinations by age band [5]

A series of line graphs showing average contacts, daily cases and deaths and cumulative vaccinations by age band.

What the modelling tells us about estimated infections as well as Hospital and ICU bed demand

The Scottish Government assesses the impact of Covid-19 on the NHS in the next few weeks in terms of estimated number of infections. Figure 10 shows two projections.

'Worse' assumes a behaviour change over a two month period following the change in restrictions on the 19th July, and the upcoming changes on the 9th of August. 'Better' assumes this behavioural change happens more gradually over a five to six month period leading to lower transmission[6].

Figure 10. Medium term projections of modelled total new daily infections, adjusting positive tests [7] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 2 nd August.

A line graph showing the short term forecast of modelled new infections.

In comparison to last week, our confidence in the recent fall in infections has increased, so the 'Worse' projection now broadly follows that fall in infections. We have also assumed a less immediate impact from the relaxations on 19 July than was assumed last week for 'Worse'.

There is uncertainty as to whether infections will increase or decrease in coming weeks. This will drive whether hospital beds and intensive care beds also continue to rise.

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.

Hospital and ICU occupancy from the June increase in cases are falling, and the future increase or decrease in hospital occupancy and intensive care use is highly uncertain, and depends on both current infection levels and the impact of the relaxation of restrictions.

Figure 11. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 2nd August.

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 [8], based on positive test data reported up to 2nd August.

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[9] (Figure 13), combining estimates from several independent models (including the Scottish Government's logistics modelling, as shown in Figures 10-12). 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 2nd August 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 2nd August. Projecting forwards is difficult when the numbers of admissions and deaths fall to very low levels, which can result in wider credible intervals reflecting greater uncertainty. The interquartile range can be used, with judgement, as the projection from which estimates may be derived until the 22nd August, albeit at lower confidence than the 90% credible interval.

These projections include the potential impact of vaccinations over the next few weeks. Modelling groups have used their expert judgement and evidence from Public Health England, Scottish Universities & Public Health Scotland, and other published efficacy studies when making assumptions about vaccine effectiveness.

Figure 13. SPI-M medium-term projection of daily hospitalisations in Scotland, including 50% and 90% credible intervals.

A combination scatter and line chart, showing the SAGE medium term projection of hospitalisations against the actual hospitalisations.

We are not projecting the numbers of people expected to die with Covid‑19 this week. The number of daily deaths has fallen to very low levels.

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 19th July 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 SPI-M 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.

Modelled rates of positive tests per 100K using data to 2nd August (Figure 14) indicate that, for the week commencing 15th August 2021, there are four local authorities with at least a 75% probability of exceeding 50 cases per 100k. These are Inverclyde, North Lanarkshire, South Lanarkshire and West Dunbartonshire. There are no local authorities which are expected to exceed 100 cases per 100k with at least a 75% probability[10].

Figure 14. Probability of local authority areas exceeding thresholds of cases per 100K (15th to 21st August 2021), data to 2nd August.

A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (15th to 21st August 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, the newest levels of wastewater Covid-19 averaged around 40-46 million gene copies per person per day, representing a decline of around 20% from last week.

The South Lanarkshire local authority overall wastewater Covid level is currently significantly above the national average, in contrast to the low levels of new cases observed there.

Figure 15 shows the national weekly aggregate for the original 28 sites (sampled from August 2020, in blue) and, from January 2021, the aggregate for the full set of 110 sampled sites (in green), with a small number of unrealistically large outliers excluded[11].

Figure 15. National average trends in wastewater Covid-19 and daily new case rates (7 day moving average) [12].

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

Figure 16 shows Shieldhall (a site covering part of Glasgow), which gave a decline in weekly wastewater Covid levels similar to the national average. Dundee also showed a decline mirroring the national level. The Edinburgh site of Seafield is experiencing a decline which is steeper than seen nationally. In contrast, the Aberdeen site of Nigg shows no decline in wastewater Covid levels from the previous week

Figure 16. Wastewater Covid-19 and daily case rate (7 day moving average) for Shieldhall (covered pop: 377k) in Glasgow [13].

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

All sites, besides Edinburgh, show wastewater Covid levels continuing to be higher than would be expected given the current rate of new cases. To some extent wastewater Covid levels should reflect not just incidence but prevalence, as those infected may have a peak in shedding but continue to shed for some time. This may partially explain how the wastewater patterns seem to lag the decline in case rates. Nevertheless, these should be interpreted cautiously, given the rapid pace of current developments and inherent uncertainty in all measures.

Of the sites with a persistent high level of Covid-19 in wastewater, Paisley in Renfrewshire (Figure 17) and Daldowie in North Lanarkshire have now both registered a measurement with a large decline. However these represent single measurements and so there remains some uncertainty.

Figure 17. Wastewater Covid-19 and daily case rate (7 day moving average) for Paisley (covered pop: 82k) in Renfrewshire.

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

Across South Lanarkshire, many sites including Hamilton, Philipshill and Allers all show levels that either have not fallen or are rising. The South Lanarkshire local authority overall (as shown in Figure 18) now is significantly above the national average, in contrast to the low levels of new cases being observed there. A similar pattern, albeit to a lesser extent, is seen in Fife, driven by sites like Kirkcaldy, Dunfermline and Levenmouth, though the data there is more uncertain.

Figure 18. Average trends in wastewater Covid-19 and daily case rates (7 day moving average) in South Lanarkshire (covered pop: 325k).

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

What estimates do we have of the number of people experiencing long Covid symptoms?

The Scottish Government has started to model the number of people likely to experience long Covid symptoms. This has then been projected forward to estimate long Covid rates in the future based on Scottish Government medium term projection modelling as set out in Figure 19.

This modelling estimates that, at 22nd August 2021, between 39,000 (0.7% of the population) and 105,000 (1.9%) people were projected to experience symptoms for 12 weeks or more after their first suspected Covid infection in Scotland.

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

Figure 19. Estimates of long Covid prevalence at 12 weeks from 16th February 2020 to 22nd August 2021 for the 5th and 25th percentile better long Covid rates (showing 95% confidence intervals). ONS estimates with range also shown.

A percentile chart showing the estimated number of long Covid prevalence at 12 weeks, compared to ONS estimates.

What next?

The modelled estimates of the numbers of new cases and infectious people will continue to be provided as measures of the epidemic as a whole, along with measures of the current point in the epidemic such as Rt and the growth rate. Further information can be found at https://www.gov.scot/coronavirus-covid-19.

We may report on exceedance in future weeks when the background levels of Covid-19 reduces so that it can be useful in identifying outbreaks.


Contact

Email: modellingcoronavirus@gov.scot