Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 51)

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. 51)
Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 51)

Coronavirus (COVID-19): modelling the epidemic in Scotland (Issue No. 51)

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 7 May 2021. The estimates in this document help the Scottish Government, the health service and the wider public sector plan and put in 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 increasing to between -3% and 0% and modelled estimates of infections now plateauing or increasing over the next three weeks. Furthermore, positive test data over the last few days appears to be showing an initial increase in Covid-19 cases, which has been taken account of in the modelling up to Monday 10 May. This increase does not as yet appear to be having an effect on hospitalisations.

There are other signs in the data reported here that this increase could continue and will be incorporated into next week's modelling. Daily contacts have increased over the last two weeks to 4.2 contacts and exceedance modelling indicates potential outbreaks in five local authority areas, which is also being reflected in the wastewater data.

Key Points

  • The reproduction rate R in Scotland is currently estimated as being between 0.8 and 1.0. This is an increase in the bottom of the range since last week.
  • The number of new daily infections for Scotland is estimated as being between 3 and 8, per 100,000 people. The top of this range has decreased since last week.
  • The growth rate for Scotland is currently estimated as being between -3% and 0%. This is an increase since last week.
  • Average contacts have increased by 27% in the last two weeks (comparing surveys pertaining to 15th - 21st April and 29th April - 5th May) with a current level of 4.2 daily contacts.
  • Contacts within the work and leisure settings (other contacts outside of the school, home and work) have increased by 74% and 43% respectively in the last two weeks.
  • All age groups have increased their contacts in the last two weeks. For those aged between 40 and 69, increases are mainly due to contacts within the work setting. For those aged under 40 and over 69, increases in contacts is linked to a rise of contacts within the other setting (contacts outside of the school, home and work).
  • Interactions between all age groups have increased or remained at a similar level in comparison to two weeks prior, with interactions between those aged 18-29 and under 18 reporting the biggest increase.
  • The biggest change in the proportion of participants visiting different locations is seen in those visiting a pub or restaurant. This has increased from less than 1% to 21% in the last two weeks, followed by visiting a non-essential shop, increasing from 22% to 35%, coinciding with the easing of restrictions on 26th April.
  • Hospital bed and ICU occupancy are projected to plateau or rise over the next few weeks, as a result of relaxations of non-pharmaceutical interventions.
  • There were five local authority areas that exceeded what would be expected at this stage in the epidemic between 5th and 11th May. Glasgow City, Midlothian, North Ayrshire, Perth & Kinross and South Lanarkshire were areas at higher risk of transmission.
  • Modelled rates per 100K indicate that for the week commencing 23 May 2021 no local authorities have at least a 75% probability of exceeding 50 cases, although Moray and Glasgow City are approaching this 75% probability.
  • The overall level of wastewater Covid-19 has continued to decline from levels reported last week at a national level. However, in some sites (in particular, Lossiemouth and Alloa) levels were higher this week than last week.

Overview of Scottish Government Modelling

Epidemiology is the study of how diseases spread within populations. One way we do this is using our best understanding of the way the infection is passed on and how it affects people who catch it to create mathematical simulations. Because people who catch Covid-19 have a relatively long period in which they can pass it on to others before they begin to have symptoms, and the majority of people infected with the virus will experience mild symptoms, this "epidemiological modelling" provides insights into the epidemic that cannot easily be measured through testing e.g. of those with symptoms, as it estimates the total number of new daily infections and infectious people, including those who are asymptomatic or have mild symptoms.

Modelling also allows us to make short-term forecasts of what may happen with a degree of uncertainty. These can be used in health care and other planning. The modelling in this research findings is undertaken using different types of data which going forward aims to both model the progress of the epidemic in Scotland and provide early indications of where any changes are taking place.

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 SAGE 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 1.

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 delivery of the vaccination programme will offer protection against severe disease and death. The modelling includes assumptions about compliance with restrictions and vaccine take-up. Work is still ongoing to understand how many vaccinated people might still spread the virus if infected. As Covid-19 is a new disease there remain uncertainties associated with vaccine effectiveness. Furthermore, there is a risk that new variants emerge for which immunisation is less effective.

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 effected by the disease and the vaccination rate for those groups.

What the modelling tells us about the epidemic as a whole

The various groups which report to the Scientific Pandemic Influenza Group on Modelling (SPI-M) use different sources of data in their models (i.e. deaths, hospital admissions, cases) so their estimates of R are also based on these different methods. SAGE's consensus view across these methods, as of 12th May, was that the value of R in Scotland was between 0.8 and 1.0 (see Figure 1). The lower limit has increased from 0.7 since last week. Particular care should be taken when interpreting this estimate as it is based on low numbers of cases, hospitalisations, or deaths and / or dominated by clustered outbreaks. They should not be treated as robust enough to inform policy decisions alone.

Figure 1. Estimates of R t for Scotland, as of 12 th May, including 90% confidence intervals, produced by SAGE. The cyan bars use Covid-19 test data and purple bars use multiple sources of data. The estimate produced by the Scottish Government (based on deaths) is the left-most (yellow), while the SAGE consensus range is the right‑most (red).

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: Scientific Advisory Group for Emergencies (SAGE).

The various groups which report to the Scientific Pandemic Influenza Group on Modelling (SPI-M) use different sources of data in their models to produce estimates of incidence (Figure 2). SPI-M's consensus view across these methods, as of 12th May, was that the incidence of new daily infections in Scotland was between 3 and 8 new infections per 100,000. The upper limit of the range has decreased since last week. This equates to between 200 and 400 people becoming infected each day in Scotland.

Figure 2. Estimates of incidence for Scotland, as of 12 th May, including 90% confidence intervals, produced by SPI-M. The cyan bars use Covid‑19 test data and purple bars use multiple sources of data. The estimate produced by the Scottish Government is the first on the left (yellow), while the SAGE consensus range is the right-most (red).

. 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: Scientific Pandemic Influenza Group on Modelling (SPI-M).

The consensus from SAGE for this week is that the growth rate in Scotland is between -3% and 0% per day. This is an increase from 5th May.

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

Average contacts have increased by 27% in the last two weeks (comparing surveys pertaining to 15th - 21st April and 29th April - 5th May) with a current level of 4.2 daily contacts as seen in Figure 3. Contacts within the work and leisure settings (contacts outside of the school, home and work) have increased by 74% and 43% respectively in the last two weeks. In contrast contacts within the home setting have decreased slightly (6%) over the same period.

Figure 3: 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 4 shows how contacts change across age group and setting. All age groups have increased their contacts in the last two weeks. This is largely driven by contacts within the work setting for those aged between 40 and 69 whereas for those aged under 40 and over 69, increases in contacts is a result of a rise of leisure contacts (contacts within the other setting).

Figure 4: 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 May 2021.

The heatmaps in Figure 5 show the mean overall contacts between age groups for the weeks relating to 15th - 21st April and 29th April - 5th May, and the difference between these periods. Interactions between all age groups have increased or remained at a similar level in comparison to two weeks prior, with interactions between those aged 18-29 and under 18 reporting the biggest increase.

Figure 5: Overall mean contacts by age group before for the weeks relating to 15 th - 21st April and 29 th April - 5 th May

Heat maps showing the mean contacts by age group in the weeks of 15 April and 29 April.

The biggest change in the proportion of participants visiting different locations is seen in those visiting a pub or restaurant. This has increased from less than 1% to 21% in the last two weeks, followed by visiting a non-essential shop, increasing from 22% to 35%, coinciding with the easing of restrictions on 26th April. The proportion of individuals visiting another's home continues to increase with a current level of 45%.

Figure 6: 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.

Vaccinations and contacts patterns

From Figure 7, it can be seen that even when contacts have increased for all age groups, cases and deaths have decreased. This coincides with the increasing number of vaccinations supplied to the population.

Figure 7: Average contacts for Panel A, daily cases and deaths [1] and cumulative vaccinations by age band [2]

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. For more on how we do this see page 4 of Issue 1 of the Research Findings[3]. Figure 8 shows two projections[4] which take account of compliance and behaviour (better and worse[5]), as well as the recent increase in infections observed in the last week.

Figure 8. Medium term projections of modelled total new infections, adjusting positive tests [6] to account for asymptomatic and undetected infections, from Scottish Government modelling, positive test data up to 8 May.

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

Figure 9 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 which are linked to Covid-19. Work is ongoing to show the modelled occupancy for stays up to a 28 day limit.

Figure 9. Medium term projections of modelled hospital bed demand, from Scottish Government modelling.

A line graph showing the short term forecast of hospital bed demand.

Figure 10 shows the impact of the projection on ICU bed demand.

Figure 10. Medium term projections of modelled ICU bed demand, from Scottish Government modelling [7].

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

SAGE produces projections of the epidemic[8] (Figure 11), combining estimates from several independent models (including the Scottish Government's logistics modelling, as shown in Figures 8-10). 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 10 May.

Modelling groups have used data from contact surveys, previous findings[9] and their own expert judgement to incorporate the impact of recent relaxations on transmission. The projections do not include the effects of any other future policy or behavioural changes.

The delay between infection, developing symptoms, the need for hospital care, and death means they will not fully reflect the impact of behaviour changes in the two to three weeks prior to 10 May. Projecting forwards is difficult when the numbers of cases, 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 for the next three weeks, albeit at lower confidence than the 90% credible interval.

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

Beyond two weeks, the projections become more uncertain with greater variability between individual models. This reflects the large differences that can result from fitting models to different data streams, and the influence of small deviations in estimated growth rates and current incidence.

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 over recent weeks. Projecting forwards is difficult when numbers fall to very low levels, therefore SPI-M-O have decided to pause producing medium term projections for daily deaths in Scotland. SPI‑M‑O's consensus view is that the number of deaths will remain very low over the next three weeks.

Figure 11. SAGE medium-term projection of daily hospitalisations in Scotland, including 50% and 90% credible intervals.

A combination scatter plot and line graph showing the SAGE medium-term projection of daily hospitalisations in Scotland, including the actuals, 50% and 90% credible intervals.

What the modelling tells us about whether Covid-19 infections exceeded what would be expected at this stage in the epidemic

Exceedance indicates whether the number of confirmed infections (based on testing) in each local authority area exceeds the number that was expected. Numbers of positive tests recorded each day, adjusted for population of each local authority and number of cases seen in preceding weeks, should fall within a certain distribution of values, which will rise and fall depending on the number of cases being seen nationally. Areas where the number of positive test results fall beyond the upper 95th percentile of this distribution may be at risk of seeing increased local transmission of Covid-19 and heightened vigilance may be required. This happens when the cumulative exceedance is higher than 6.0. See the Technical Annex in issue 47 for more information.

Figures 12 and 13 show exceedance for local authority areas. Recent cumulative exceedance highlights Glasgow City (exceedance = 7.34), Midlothian (6.58), North Ayrshire (5.39), Perth & Kinross (4.01), and South Lanarkshire (3.68) as areas at higher risk of transmission.

Figure 12. Map of cumulative weekly exceedance to 11th May, for Scottish Local Authorities.

A map of cumulative exceedance to 11 May, for Scottish Local Authorities.

Figure 13. Graphs of daily and cumulative exceedance for the local authorities deemed as higher risk over the period 5 th to 11 th May.

Nine line graphs of daily and cumulative exceedance for the local authorities deemed as higher risk over the period 5 – 11 May.

Figure 14 shows the daily and cumulative exceedance for Moray. Exceedance analysis identifies emerging issues, so it does not highlight local authority areas if the rate of cases has been elevated for a longer period, or if the national rate has increased and become closer to that of a local authority previously showing exceedance. The figure indicates that the exceedance for Moray has reduced since last week and now falls in the range of expected values for this point in the epidemic.

Figure 14. Daily and cumulative exceedance for Moray local authority over the period 5 th to 11 th May.

A line graph of daily and cumulative exceedance for Moray local authority over the period 5 – 11 May.

What we know about which local authorities are likely to experience high levels of Covid-19 in two weeks' time

We are using modelling based on Covid-19 cases and deaths 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 are predicted to exceed a threshold, e.g. 500 cases.

Modelled rates per 100K (Figure 15) indicate that for the week commencing 23 May 2021, no local authorities have at least a 75% probability of exceeding 50 cases, although Moray and Glasgow City are approaching this 75% probability.

Figure 15. Probability of local authority areas having more than 50, 100, 300 or 500 cases per 100K (23 – 29 May 2021).

A series of four maps showing the probability of local authority areas having more than 50, 100, 300 or 500 cases per 100K (23 – 29 May).

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

Levels of Covid-19 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 daily 7-day average positive 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 were slightly down this week compared to last week, in contrast to case rates which rose slightly. However, in some sites (in particular, Lossiemouth and Alloa) levels were higher this week than last week.

Figure 16 shows the national aggregate for the original 28 sites with long‑term records (in blue) and, from January 2021, the aggregate for the full set of up to 106 currently sampled sites (in green). Both sets of sites show a small decline in WW Covid-19.

Figure 16. National average trends in wastewater Covid-19 and daily case rates (7 day moving average). An anomalously high value in Seafield (Edinburgh) in mid-February is removed. See Issue 40 for details.

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

Figure 17 shows the data with a smoothed curve for Shieldhall, one of the largest and most sampled sites. Note that while the most recent case data for Shieldhall shows a rise in cases, it is unclear whether this rise is indicative of a change in the trend for this site. A change of this size is well within the level of random variability for Shieldhall's WW Covid-19 levels. Hence the fact that cases rose recently while WW Covid-19 fell from the spike at the start of May should be interpreted with caution.

Figure 17. Wastewater Covid-19 and daily case rate (7 day moving average) for Shieldhall in Glasgow City (pop: 377k) The black line and red shaded area provide a smoothed curve and confidence interval

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

In contrast, for Lossiemouth in Moray (Figure 18) both wastewater Covid‑19 and case rates have risen greatly recently, suggesting a resurgence of the virus in the locality. However the most recent wastewater reading shows a low level of virus, though this particular reading is not adjusted for dilution due to the lack of flow and ammonia data. Meanwhile, Alloa in Clackmannanshire (Figure 19) shows a rise in WW Covid-19 levels in excess of the more modest rise in case rates. This suggests that this is a location of concern. Both Lossiemouth and Alloa are fairly large sites (with 38 and 35 thousand inhabitants respectively in each of their catchment areas) that appear to be bucking the national trend.

Figure 18. Wastewater Covid-19 and daily case rate (7 day moving average) for Lossiemouth in Moray (pop: 38k)

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

Figure 19. Wastewater Covid-19 and daily case rate (7 day moving average) for Alloa in Clackmannanshire (pop: 35k)

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

The exceedance modelling has indicated that there are some local authorities that are at a higher risk of transmission and could indicate potential outbreaks. A rise in cases has already been observed in Shieldhall in Glasgow City in Figure 17. Figures 20 and 21 show a similar picture for Penicuik in Midlothian and Fairlie in North Ayrshire. WW data for the other local authorities indicated in the exceedance modelling (Perth & Kinross, and South Lanarkshire) suggest a plateauing of cases. Note that the WW and exceedance data do not cover the same periods and so an uptick in WW data may be observed next week.

Figure 20. Wastewater Covid-19 and daily case rate (7 day moving average) for Penicuik in Midlothian (pop: 12k)

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

Figure 21. Wastewater Covid-19 and daily case rate (7 day moving average) for Fairlie in North Ayrshire (pop: 2k)

A line chart showing average trends in wastewater Covid-19 and daily case rates for Fairlie in North Ayrshire.

What next?

The Scottish Government continues to work with a number of academic modelling groups to develop other estimates of the epidemic in Scotland.

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.

Analysis from the EAVE 2 group, which tells us about the pattern of demographics and clinical risk groups over time for those who are testing positive with Covid-19, will be provided in future issues.


Contact

Email: modellingcoronavirus@gov.scot