Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 74)

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. 74)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 74)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 74)

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 14th October 2021. The estimates in this document help the Scottish Government, the health service and the wider public sector plan and put into place what is needed to keep us safe and treat people who have the virus.

This edition of the research findings focuses on the epidemic as a whole, looking at estimates of R, growth rate and incidence as well as local measures of change in the epidemic.

In Scotland, the modelled estimate for R is between 0.8 and 1.0, with the growth rate between -3% and 0%.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.8 and 1.0, as of 5th October. This is unchanged from last week.
  • The number of new daily infections for Scotland is estimated as being between 77 and 114, per 100,000 people. The lower and upper limits have decreased since last week.
  • The growth rate for Scotland is currently estimated as between -3% and 0%. This is unchanged from last week.
  • Average contacts have decreased by approximately 14% in the last two weeks (comparing surveys pertaining to 23rd September - 29th September and 7th October - 13th October) with a current level of 4.7 daily contacts.
  • Mean contacts within the work setting have decreased by around 48% whereas contacts in the other setting (contacts outside home, school and work) have increased by 11% in the last two weeks. Contacts within the home have remained at a similar level over the same period.
  • Those aged between 30-39 have reported the biggest decrease in interactions with those aged under 18 in the last two weeks whereas interactions between the 18-29 age group with those under 18 has shown the biggest increase.
  • The proportion of individuals visiting another's home decreased from approximately 51% to 44% whilst individuals visiting a pub or restaurant rose from 45% to 47% 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 66%.
  • The number of people wearing a face covering where they have at least one contact outside of the home has fallen from 87% to 80% in the last two weeks.
  • Hospital and ICU occupancies are in a gradual fall or 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 18th October indicate that, for the week commencing 31st October 2021, there are 28 local authorities which are expected to exceed 50 cases per 100K with at least 75% probability. There are 23 local authorities which are 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, after the decrease observed last week (5th to 11th October 2021), levels of Covid in wastewater have remained consistent.
  • Modelling of long Covid estimates that on 7th November 2021 between 1.2% and 2.6% 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 and lower limits of the estimate are higher than last week.

Recent cases

Figure 1 shows the number of Covid-19 cases reported in Scotland between July and October 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 20th October 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 5th October (dashed line 1). The Scottish Contact Survey uses data to 13th October (dashed line 2). The medium term projections and modelled rates of positive tests per 100K use data to 18th October (dashed line 3). Wastewater analysis uses data to 19th October (dashed line 4). The Scottish Government modelling of infections, hospitalisations and ICU beds, the long Covid analysis use data to 20th October (dashed line 5).

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 5th October[2] in Scotland was between 0.8 and 1.0 (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 5 th 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 5th October, was that the incidence of new daily infections in Scotland was between 77 and 114 new infections per 100,000. This equates to between 4,200 and 6,200 people becoming infected each day in Scotland. The lower and upper limits have decreased since last week.

Figure 3. Estimates of incidence for Scotland, as at 5 th 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 -3% and 0% per day as at 5th October. The lower and upper limits are unchanged since last week.

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

Average contacts have decreased by approximately 14% in the last two weeks (comparing surveys pertaining to 23rd September - 29th September and 7th October - 13th October) with a current level of 4.7 daily contacts as seen in Figure 4. Mean contacts within the work have decreased by around 48% whereas contacts in the other setting (contacts outside home, school and work) have increased by 11% in the last two weeks. Contacts within the home 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 60 and over reported an increase in overall contacts whereas all remaining age groups reported a decrease. The decreases are largely driven by a reduction in contacts within the work 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 October 2021.

The heatmaps in Figure 6 show the mean overall contacts between age groups for the weeks relating to 23rd September - 29th September and 7th October - 13th October and the difference between these periods. Those aged between 30-39 have reported the biggest decrease in interactions with those aged under 18 in the last two weeks whereas interactions between the 18-29 age group with under 18's has shown the biggest increase.

Figure 6. Overall mean contacts by age group before for the weeks relating to 23rd September - 29th September and 7th October - 13th October.
Figure 6. Heat maps showing the mean contacts by age group in the weeks of 23 September and 7 October.

The biggest differences are seenwith those visiting a another's home and also individuals visiting a pub or restaurant (Figure 7). The proportion of individuals visiting another's home decreased from approximately 51% to 44% while individuals visiting a pub or restaurant rose from 45% to 47% 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. Proportion of participants reported indoors and outdoors for contacts individually reported for panel B. The proportion of contacts reported to have been indoors only has remained at similar level to two weeks prior, currently at 66%.
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 has fallen from 87% to 80% in the last two weeks.

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)

From Figure 10, it can be seen that the oldest age group has lower levels of contacts and higher vaccinations than the youngest age group, they also have the lowest weekly case number comparatively to the younger age group. Despite that they have higher weekly hospitalization levels to that seen with the younger age groups.

Figure 10. Average contacts for Panel B, weekly cases, covid-19 hospital admissions and deaths [5] and cumulative vaccinations by age band [6]
Figure 10. 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 11 shows three projections over the three weeks to 7th 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[7]. All three scenarios account for the end of the half-term period and the start of the COP 26 conference beginning in Glasgow 31st October. Due to this, there is a large amount of uncertainty as to the potential impact on infections.

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

Figure 11. Medium term projections of modelled total new daily infections, adjusting positive tests [8] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 20th October. The chart on the right hand side is a cut out of the one on the left but with the y axis maximum set to 20,000.
Figure 11. A line graph showing the short term forecast of modelled new infections.

Figure 12 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 12. Medium term projections of modelled hospital bed demand, from Scottish Government modelling, based on positive test data reported up to 20th October.
Figure 12. A line graph showing the short term forecast of hospital bed demand.

Figure 13 shows the impact of the projection on ICU bed demand.

Figure 13. Medium term projections of modelled ICU bed demand, from Scottish Government modelling [9], based on positive test data reported up to 20th October.
Figure 13. 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[10] (Figures 14 and 15), combining estimates from several independent models (including the Scottish Government's logistics modelling, as shown in Figures 11 to 13). 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 18th October 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 18th October. 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 9th November.

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

Figure 14. SPI-M medium-term projection of daily hospitalisations in Scotland, at 50% credible intervals [11].
Figure 14. A combination scatter and line chart, showing the SAGE medium term projection of hospitalisations against the actual hospitalisations.
Figure 15. SPI-M medium-term projection of daily deaths in Scotland, at 50% credible intervals.
Figure 15. 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 18th October 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.

Modelled rates of positive tests per 100K using data to 18th October (Figure 16) indicate that, for the week commencing 31st October 2021, there are 28 local authorities which are expected to exceed 50 cases per 100K with at least 75% probability[12].

There are 23 local authorities which are 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[13].

Figure 16. Probability of local authority areas exceeding thresholds of cases per 100K (31 st October to 6 th November 2021), data to 18th October.
Figure 16. A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (5th to 11th September 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 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, levels of wastewater Covid-19 remained at a similar level to the previous week, around 56 million gene copies per person per day (Mgc/p/d) in the week ending 19th October 2021. This is in line with the numbers of cases that can be seen in the same time period.

Figure 17 shows the national running average trend (over a 7-day period) for the full set of sampled sites, with a small number of unrealistically large outliers excluded. Covid-19 levels have stabilised. As also seen last week, the ratio of WW levels to case numbers is now closer to 1 Mgc/p/d corresponding to 1 new case per 100K inhabitants per day, a relationship that historically has been seen at most times, except during peaks. Wastewater Covid levels are now similar to those during the winter peak in early January.

Figure 17. National running average trends in wastewater Covid-19 and daily new case rates (7 day moving average), with samples taken up until 19th October 2021 [14].
Figure 17. A line chart showing national average trends in wastewater Covid-19 and daily case rates.

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

The Scottish Government is modelling the number of people likely to experience long Covid symptoms. This gives a projection of estimated self-reported long Covid rates in the future, based on Scottish Government medium term projection modelling, as set out in Figure 18.

This modelling estimates that at 7th November 2021 between 64,000 (1.2% of the population) and 140,000 (2.6%) people are projected to self-classify with long Covid 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 18. Estimates of self-classified long Covid prevalence at 12 weeks from 16th February 2020 to 7 th November 2021 (showing 90% confidence interval). ONS estimates of self-reported long Covid with range also shown.
Figure 18. 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