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Coronavirus (COVID-19): modelling the epidemic (issue no.82)

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.

This document is part of a collection


Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 82)

Background

This is a report on the Scottish Government modelling of the spread and level of Covid-19 in Scotland. This updates the previous publication on modelling of Covid-19 in Scotland published on 10th December 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. It looks at both the impact of the Delta and Omicron variants. We will update on a weekly basis as we know more about the Omicron variant.

Key Points

Based on at point when the Delta variant made up the majority of cases

  • The reproduction rate R in Scotland is currently estimated as being between 0.9 and 1.1, as of 30th November. This is unchanged since last week.
  • The number of new daily infections for Scotland is estimated as being between 96 and 128 as at 30th November, per 100,000 people.
  • The growth rate for Scotland is currently estimated as between -2% and 2% as at 30th November. The lower and upper limits have increased since last week.
  • This report normally contains three elements: UKSHA consensus, Scottish Government projections and SPI-M projections. Due to uncertainty surrounding the Omicron variant and its increasing prevalence across the UK, SPI-M has been unable to produce consensus medium-term projections for hospital admissions and deaths this week.
  • Modelled rates of positive tests per 100K using data to 13th December indicate that, for the week commencing 26th December 2021, 29 of the 32 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. The exceptions are Na h-Eileanan Siar, Orkney Islands and Shetland Islands. These 29 local authorities are also expected to exceed 100 cases per 100K with at least 75% probability. Twelve local authorities are expected to exceed 300 cases per 100K with at least 75% probability. Only one local authority, East Ayrshire, is expected to exceed 500 cases per 100K with at least 75% probability. These models are based on a projection where the Delta variant makes up the majority of cases. Therefore it is likely that due to the Omicron variant, these are likely to be an underestimate.
  • Modelling of long Covid estimates that on 2nd January 2022 between 1.5% and 3.2% 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 of the proportion of the population with long Covid is higher than last week.
  • Nationwide, wastewater Covid-19 RNA levels have shown a decrease of around 21% from the elevated levels seen in the last two weeks. The week ending 14th December saw levels of around 58 million gene copies per person per day (Mgc/p/d), down from around 74 Mgc/p/d in the previous week. It should be noted that this decrease is in the context of decreasing Delta variant and increasing Omicron variant.

Based on the Omicron variant

  • Infections are rising and the number of infections are expected to continue to rise in the coming weeks as Omicron becomes more dominant. In three weeks' time we estimate that daily infections may be between 15,000 and 130,000.
  • Using data to 14th December, we can estimate a doubling time for Scotland of between 2.36 – 2.48 days using S-gene target failure as a proxy for Omicron cases.
  • Given this doubling time, it is likely that only a small percentage of infections will be of the Delta variant by January 2022.

Other modelling

  • Average contacts from the most recent Panel B cohort of the Scottish Contact Survey (week ending 8th December) indicate an average of 4.8 contacts.
  • Mean contacts within the other setting (contacts outside home, school and work) have increased by 14% whereas work contacts have decreased by 12% in the last two weeks. Contacts within the home have remained at a similar level over the same period.
  • Those aged 60 and over have increased their contacts within the last week with the majority of their contacts taking place within the other setting (contacts outside home, school and work). All remaining groups have reduced or have maintained a similar level of contacts over the same period.
  • The highest interactions are reported between those 70 and over with each other. The biggest decrease in interactions is between the those under 18 with individuals within the 18-29 age group in the last two weeks.
  • Visits to another's home decreased from approximately 49% to 45% and attending an outside event decreased from 71% to 68% in the last two weeks.
  • Approximately 63% of individuals have taken at least one lateral flow test within the last 7 days for the survey pertaining to the 2nd – 8th December.
  • The youngest and oldest age groups (18-29 and 70+) have reported the lowest proportions of individuals who have taken one or more lateral flows, with at most 54% taken at least one. In contrast, those aged between 30-59 report the highest proportion of individuals taking at least one lateral flow test within the last 7 days, with at least 70% taken at least one.

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 16th December 2021

A bar 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 30th November (dashed line 1). The Scottish Contact Survey uses data to 8th December (dashed line 2).

The Scottish Government modelling of infections, hospitalisations and ICU beds, the long Covid analysis, and the modelled rates of positive tests per 100K use data to 13th December (dashed line 3). Wastewater analysis used data to 14th December (dashed line 4).

Figure 2 shows the number of confirmed Omicron cases and those cases that are under investigation. Note that data for 9th -12th December is lagged due to specimen processing times and these will be undercounted.

Figure 2: Confirmed Omicron variants and cases under investigation in Scotland, data to 12th December by specimen date [1]

A bar chart showing the number of confirmed Omicron cases and cases under investigation in Scotland.

Source: Public Health Scotland COVID-19 & Winter Statistical Report

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 change in the epidemic, e.g. any impact of the Omicron variant. Therefore a new section has been included covering what we know of this variant.

The first section of this report covers a range of modelling from a point when the Delta variant made up the majority of cases:

  • The UK Health Security Agency (UKHSA) consensus is shown, which uses a range of data in its estimates of R and the growth rate.

The second section of this report covers Omicron:

  • Looking at estimates of the doubling time of this variant, using the data available for Scotland.
  • It also projects this forward into the future to estimate the proportion of Omicron cases in the coming weeks.
  • The logistical model has been updated to incorporate both Delta and Omicron. The results are split down by age group, and the model is used to give a projection of the number of people that will be infected.

We also include in this report other modelling:

  • The Scottish Contact Survey (SCS) is used 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.
  • We also report on levels of Covid-19 RNA in wastewater around Scotland and compare it to the 7-day average daily new cases.

What the modelling tells us about the epidemic at a point in time when Delta made up the majority of cases

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. These are based on data to 13th December.

UKHSA's consensus view across these methods, was that the value of R as at 30th November[2] in Scotland was between 0.9 and 1.1 (see Figure 3)[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 3 and 4.

Figure 3. Estimates of R t for Scotland, as of 30th November, including 90% confidence intervals, produced by EMRG [4].

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 4). UKHSA's consensus view across these methods, as at 30th November, was that the incidence of new daily infections in Scotland was between 96 and 128 new infections per 100,000. This equates to between 5,200 and 7,000 people becoming infected each day in Scotland.

Figure 4. Estimates of incidence for Scotland, as at 30th 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 30th November. The lower and upper limits have increased since last week.

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 13th December 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. Models have varying degrees of responsiveness to sudden changes in case trends, therefore there is an increased level of uncertainty in local authorities in which there have been recent sharp increases in case numbers.

Modelled rates of positive tests per 100K using data to 13th December (Figure 5) indicate that, for the week commencing 26th December 2021, 29 of the 32 local authorities are expected to exceed 50 cases per 100K with at least 75% probability. The exceptions are Na h-Eileanan Siar, Orkney Islands and Shetland Islands.

These 29 local authorities are also expected to exceed 100 cases per 100K with at least 75% probability.

Twelve local authorities are expected to exceed 300 cases per 100K with at least 75% probability. These are Edinburgh, East Ayrshire, East Dunbartonshire, Falkirk, Glasgow, North Ayrshire, North Lanarkshire, Renfrewshire, South Ayrshire, South Lanarkshire, West Dunbartonshire and West Lothian.

Only one local authority, East Ayrshire, is expected to exceed 500 cases per 100K with at least 75% probability[5].

These models are based on a projection where the Delta variant makes up the majority of cases. Therefore it is likely that due to the Omicron variant, these are likely to be an underestimate.

Figure 5. Probability of local authority areas exceeding thresholds of cases per 100K (26th December 2021 to 1st January 2022), data to 13th December.

A series of four maps showing the probability of local authority areas exceeding thresholds of cases per 100K (26th December 2021 to 1st January 2022).

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

Due to uncertainty surrounding the Omicron variant and its increasing prevalence across the UK, SPI-M-O has been unable to produce consensus medium-term projections for hospital admissions and deaths this week. The delay between infection, developing symptoms, the need for hospital care and death means the epidemiological data cannot fully reflect the recent rapid increase of the Omicron variant. SPI-M-O hopes to produce medium-term projections again in the near future when the impact of Omicron is better reflected in the epidemiological data.

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 9.

This modelling estimates that at 2nd January 2022 between 82,000 (1.5% of the population) and 176,000 (3.2%) 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 of the proportion of the population with long Covid 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 6. Estimates of self-classified long Covid prevalence at 12 weeks from 16th February 2020 to 2nd January 2022 (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 we know about the Omicron variant

As of 12th December 2021, a total of 4,252 cases have been reported, of which 186 (4.4%) were confirmed, 56 (1.3%) were highly probable and 4,010 (94.3%) were possible. Total cases are more than ten-fold higher than on 5th December, when there were 389[6].

Based on data to 14th December, we can estimate a doubling time for Scotland of between 2.36 – 2.48 days using S-gene target failure as a proxy for Omicron cases. We will continue to monitor the doubling times which may fluctuate or change over future days.

Figure 7: Estimated proportion of Omicron cases in Scotland based on S-gene target failure, data to 14th December

A line chart showing the estimated probability of S-gene target failure and it’s growth since mid-November.

This curve is projected to estimate the proportion of Omicron cases in future weeks in Scotland.

Figure 8: Estimate of the proportion of Omicron cases in Scotland in the coming weeks

A projection of the estimated probability of S-gene target failure, showing that most cases in Scotland are expected to be of Omicron variant by mid December to early January.

See the Technical Annex for information about the methodology.

What the modelling tells us about estimated infections

The Scottish Government assesses the impact of Covid-19 on the NHS in the next few weeks, in this research findings we focus on estimating the number of infections. Figures 9-11 show three projections over the three weeks to 2nd January, broken down by possible Omicron infections, Delta infections, and combined infections. We hope to be able to provide hospitalisation and ICU in future weeks which account for the Omicron variant as well as Delta.

These projections include the effect of the new interventions announced on 14th December. 'Central' assumes a continuation of the current trend for Delta, and that Omicron is around three times more transmissible. 'Worse' assumes a higher transmissibility for both Delta and Omicron. 'Better' assumes a lower transmissibility for both variants. All projections also assume a lower vaccine effectiveness[7] for Omicron than for Delta[8].

Delta infections are likely to fall over time, but those still being infected and already infected will still contribute to the numbers of people in hospital and ICU. Meanwhile the increase which we see in Omicron infections will continue. At the present time, due to the lag between infections and hospitalisations, only infections figures are provided in Figures 9-11. We hope to be able to provide hospital occupancy and ICU in future weeks.

Figure 9. Medium term projections of modelled total new combined daily infections in Scotland, adjusting positive tests [9] to account for asymptomatic and undetected infections, from Scottish Government modelling, based on positive test data reported up to 13th December

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

Figure 10. Medium term projections of modelled total new Delta daily infections in Scotland, adjusting positive tests to account for asymptomatic and undetected infections, from Scottish Government modelling, based on S-gene positive data reported up to 13th December

A line graph showing the short term forecast of modelled new infections for Delta variant only.

Figure 11. Medium term projections of modelled total new Omicron daily infections in Scotland, adjusting positive tests to account for asymptomatic and undetected infections, from Scottish Government modelling, based on S-gene negative data reported up to 13th December

A line graph showing the short term forecast of modelled new infections for Omicron variant only.

The methodology for estimating projections is included in the Technical Annex.

Other modelling

This section covers some modelling outputs for which the methodology is not affected by which variant is dominant.

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 8th December) indicate an average of 4.8 contacts. This has decreased by 8% compared to the previous Panel B of the survey (week ending 24th November), as seen in Figure 12.

Mean contacts within the other setting (contacts outside home, school and work) have increased by 14% whereas work contacts have decreased by 12% in the last two weeks. Contacts within the home have remained at a similar level over the same period.

Figure 12: 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 13 shows how contacts change across age group and setting. Those aged 60 and over have increased their contacts within the last week with the majority of their contacts taking place within the other setting (contacts outside home, school and work). All remaining groups have reduced or have maintained a similar level of contacts over the same period.

Figure 13: 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 14 show the mean overall contacts between age groups for the weeks relating to 18th November - 24th November and 2nd December - 8th December and the difference between these periods. The highest interactions are reported between those 70 and over with each other. In the last two weeks, the biggest decrease in interactions is between those under 18 with individuals within the 18-29 age group.

Figure 14: Overall mean contacts by age group before for the weeks relating to 18th November - 24th November and 2nd December - 8th December.

Heat maps showing the mean contacts by age group in the weeks beginning 4th November and 18th November.

As shown in Figure 15, the biggest changes in the proportion of participants visiting different locations, though slight, is seen in those visiting another's home and attending an event outside. Visits to another's home decreased from approximately 49% to 45% and attending an outside event decreased from 71% to 68% in the last two weeks. A breakdown of this by age and gender is given in the Technical Annex.

Figure 15: 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.

Approximately 63% of individuals have taken at least one lateral flow test within the last 7 days for the survey pertaining to the 2nd – 8th December as shown in Figure 16. The youngest and oldest age groups (18-29 and 70+) have reported the lowest proportions of individuals who have taken one or more lateral flows, with at most 54% taken at least one. In contrast, those aged between 30-59 report the highest proportion of individuals taking at least one lateral flow test within the last 7 days, with at least 70% taken at least one.

Figure 16: Number of days participants taken a lateral flow in last 7 days

A bar chart showing the number of days in which participants have taken a lateral flow test over the last seven days.

Figure 17: Number of days participants taken a lateral flow in last 7 days by age group

A series of bar charts showing the number of days in which participants have taken a lateral flow test over the last seven days, by age.

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 shown a decrease from the elevated levels seen in the last two weeks. The week ending on 14th December saw levels of around 58 million gene copies per person per day (Mgc/p/d), down from around 74 Mgc/p/d in the previous week (week ending 7th December), a decrease of 21%. It should be noted that this decrease is in the context of decreasing Delta variant and increasing Omicron variant. The Office of National Statistics' Coronavirus Infection Survey (CIS) has shown a similar recent drop, although data are only available up until 1st December. Case rates have continued their increase from last week.

Figure 18 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 have dropped slightly while an increase in case rates can be observed across almost all sites. This national trend is not representative for all sites though: Figure 19 shows Dalmuir (covered pop: 428k) in Glasgow, where increases in both wastewater viral levels and case rates are seen.

Figure 18. National running average trends in wastewater Covid-19 and daily new case rates (7-day moving average) up until 10th December [10].

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

Figure 19. Wastewater Covid-19 and daily case rate (7 day moving average) for Dalmuir (covered pop: 428k) in Glasgow [11].

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

What next?

Modelling will be provided for both the Delta and Omicron variants where possible. As more information on Omicron becomes available this will be incorporated in the different models as and when it is appropriate to do so.

Contact

Email: modellingcoronavirus@gov.scot

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