Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 49)

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.

23 page PDF

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23 page PDF

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Contents
Coronavirus (COVID-19): modelling the epidemic (issue no. 49)
Overview of Scottish Government Modelling

23 page PDF

1.1 MB

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 which 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 affected 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 28th April, was that the value of R in Scotland was between 0.8 and 1.0 (see Figure 1). The lower and upper limits have increased from last week. Particular care should be taken when interpreting these estimates as they are based on low numbers of cases and deaths, and so should not be treated as robust enough to inform policy decisions alone.

Figure 1: Estimates of R t for Scotland, as of 28 th April, including 90% confidence intervals, produced by SAGE. The blue bars are death-based models, purple use multiple sources of data and cyan uses Covid-19 test results. The estimate produced by the Scottish Government is the third from left (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. The blue bars are death-based models, purple use multiple sources of data and cyan uses Covid-19 test results. The estimate produced by the Scottish Government (a deaths and cases-based model) is the 3rd from left (yellow). The R value estimated by the Scottish Government is similar to the estimates of other groups using models which draw upon numbers of deaths. The SAGE consensus, shown at the right hand side of the plot, is that the most likely range is between 0.8 and 1.0.

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). The Scottish Government results this week have been computed using a platform called Epidemia (see Technical Annex in issue 37) which expands the Bayesian semi-mechanistic model which the Scottish Government runs. SPI-M's consensus view across these methods, as of 28th April, was that the incidence of new daily infections in Scotland was between 1 and 15 new infections per 100,000. The limits of the range are lower than last week. This equates to between 50 and 800 people becoming infected each day in Scotland.

Figure 2: Estimates of incidence for Scotland, as of 28 th April, including 90% confidence intervals, produced by SPI-M. The blue bar is a death‑based model and the purple bars represent models which use multiple sources of data. The estimate produced by the Scottish Government (a semi-mechanistic model) is the second from 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. The blue bar is a death based model (1st from left). The purple bars (3rd to 6th from the left) use multiple sources of data. The estimate produced by the Scottish Government (a deaths-based model) is the 2nd from the left (yellow). The SAGE consensus is shown at the right hand side of the plot, between 1 and 15.

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 -4% and -1% per day. The range is unchanged from 21st April.

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

Average contacts are higher than seen during the lockdown period (averaging around 3 daily contacts) and have increased slightly in the last two weeks, with a current level of 3.3 daily contacts as seen in Figure 3. Contacts within the work and school setting have shown a decrease in the last two weeks (comparing surveys pertaining to 1st - 7th April and 15th - 21st April) by 32% and 88% respectively. In contrast, mean contacts within the 'other' setting (contacts outside of the school, home or work settings) have increased by approximately 11% over the same period.

Figure 3: Mean Adult Contacts (truncated at 100) from SCS.
A line graph showing mean adult contacts by age group for panel A and panel B in the work setting from 6 Aug to 21 Apr.

Figure 4 shows how contacts change across age group and setting. Individuals aged 60 and over have increased their contacts in the last two weeks, largely driven by contacts within the 'other' setting while average contacts for those aged under 60 have remained level or have shown a decrease in the last two weeks due to reductions in contacts within the work 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 6 Aug to 21 Apr.

The heatmaps in Figure 5 show the mean overall contacts between age groups for the weeks relating to 1st – 7th April and 15th – 21st April, and the difference between these periods. The 18-39 age group has shown a decrease in interactions with individuals under 18 whereas those aged 40-49 have increased their interactions with this age group.

Figure 5: Overall mean contacts by age group for the weeks relating to 1st - 7th April and 15th – 21st April.
Heat maps showing the mean contacts by age group in the weeks of 1 Apr and 15 Apr.

The biggest change in the proportion of participants visiting different locations is seen in those visiting a hairdressers/beauticians (Figure 6). This has increased from less than 1% to 20% in the last two weeks, followed by visits to non-essential shops, increasing from 14% to 22%, coinciding with the easing of restrictions on 5th April. Contacts within another's home continues to increase since the start of January, rising from 21% in January to 41% for the most recent survey.

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 where contacts have remained consistent or even increased for the older 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 [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. For more on how we do this see page 4 of Issue 1 of the Research Findings[6]. Figure 8 shows two projections[7] which take account of compliance and behaviour (better and worse[8]).

Figure 8: Medium term projections of modelled total new infections, adjusting positive tests [9] to account for asymptomatic and undetected infections, from Scottish Government modelling, positive test data up to 24 April.
A line graph showing the short term forecast of modelled new infections. The forecast indicates just over 5,000 infections in four weeks.

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. The forecast indicates up to around 350 may be required in four weeks.

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 [10].
A line graph showing a short term forecast of modelled ICU bed demand, from Scottish Government modelling. This shows up to around 20 ICU may be required in four weeks.

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[11] (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 26 April.

Modelling groups have used data from contact surveys, previous findings[12] and their own expert judgement to incorporate the impact of re‑opening schools and the Easter holidays 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 26 April. 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 four weeks, albeit at lower confidence than the 90% credible interval.

These projections include the potential impact of vaccinations over the next four 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 four 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 we know about first dose mass vaccination reducing COVID-19 hospitalisations

The Early Pandemic Evaluation and Enhanced Surveillance of COVID-19 (EAVE) 2 Study Group[13] have updated the pattern of demographics and clinical risk groups over time for those who have been hospitalised with COVID-19 in Scotland (see Technical Annex in issue 34 of the Research Findings).

A major study reported in the Lancet[14] investigated the association between mass roll-out of the first doses of vaccines and hospital admissions in Scotland for COVID-19.

As part of EAVE 2 – a BREATHE-associated project – researchers from the Universities of Edinburgh, Strathclyde, Aberdeen, Glasgow, and St Andrews, and Public Health Scotland (PHS) analysed a dataset covering the entire Scottish population of 5.4 million people to track the vaccine roll-out in real time.

During the study analysis period (between 8th Dec 2020 and 22nd Feb 2021) over 1.33 million people were vaccinated. The mean age of those vaccinated was 65.0 years.

Four weeks after receiving a first dose, the Pfizer-BioNTech vaccine was shown to reduce the risk of COVID-19 hospitalisation by 91% (95% CI 85–94), and the Oxford-AstraZeneca vaccine by 88% (95% CI 75–94). These results show an association with substantial reductions in the risk of COVID-19 hospitalisations across Scotland.

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 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 Dumfries and Galloway (exceedance = 7.62), Moray (4.44), Inverclyde (3.43) and Glasgow City (3.08) as areas of higher risk of transmission.

Figure 12: Map of cumulative weekly exceedance to 26 April, for Scottish Local Authorities.
A map of cumulative exceedance to 26 April, for Scottish Local Authorities.
Figure 13: Graphs of daily and cumulative exceedance for the local authorities deemed as higher risk over the period 20 – 26 April.
Four line graphs of daily and cumulative exceedance for the local authorities deemed as higher risk over the period 06 – 12 April. The period covered is 21 March to 12 April.

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 14) indicate that for the week commencing 9 May 2021, no local authorities have at least a 75% probability of exceeding 50 cases. This is the same as last week. Please note that the local estimates should be interpreted with caution as they are based on fewer models than previous reports.

Figure 14: Probability of local authority areas having more than 50, 100, 300 or 500 cases per 100K (9 – 15 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 (9 - 16 May 21).

Contact

Email: modellingcoronavirus@gov.scot