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Coronavirus (COVID-19): modelling the epidemic (issue no. 56)

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


Technical Annex

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.

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.

Better and Worse Scenarios

Due to the large areas of uncertainty around the path of the epidemic, both in how many people could be affected and in how quickly it could happen, we provide two projections for estimated infections and hospital demand, illustrating what might happen in two broad scenarios.

In this issue, the difference between the Better and Worse scenarios illustrates the difference between different hospital lengths of stay (Worse, remaining the same for Delta as it was for Alpha, and Better, with a reduced length of stay) for the Delta variant. The number of infections are assumed to be the same in both projections.

Both scenarios cover the same wide range of behavioural patterns, from decreased mixing in comparison to now to increased mixing.

How the modelling compares to the real data as it emerges

The following charts show the history of our modelling projections in comparison to estimates of the actual data. The infections projections were largely accurate during October to mid-December and from mid‑January onward. During mid-December to mid-January, the projections underestimated the number of infections, due to the unforeseen effects of the new variant.

Figure 18. Infections projections versus actuals, for historical projections published between one and three weeks before the actual data came in.
Figure 18. A combination line and scatter graph comparing infections projections against actuals.

Hospital bed projections have generally been more precise than infections estimates due to being partially based on already known information about numbers of current infections, and number of people already in hospital. The projections are for number of people in hospital due to Covid-19, which is slightly different to the actuals, which are number of people in hospital within 28 days of a positive Covid-19 test.

Figure 19. Hospital bed projections versus actuals, for historical projections published between one and three weeks before the actual data came in.
Figure 19. A combination line and scatter graph comparing hospital bed occupancy projections against actuals.

As with hospital beds, ICU bed projections have generally been more precise than infections. The projections are for number of people in ICU due to Covid-19. The actuals are number of people in ICU within 28 days of a positive Covid-19 test up to 20 January, after which they include people in ICU over the 28 day limit.

Figure 20. ICU bed projections versus actuals, for historical projections published between one and three weeks before the actual data came in.
Figure 20. A combination line and scatter graph comparing ICU occupancy projections against actuals.
Table 1. Probability of local authority areas having more than 50, 100, 300 or 500 cases per 100K (27 June to 3 July 2021) [14].
LA P (Cases > 500) P (Cases > 300) P (Cases > 100) P (Cases > 50)
Aberdeen City 15-25% 25-50% 75-100% 75-100%
Aberdeenshire 5-15% 5-15% 25-50% 75-100%
Angus 50-75% 75-100% 75-100% 75-100%
Argyll and Bute 0-5% 5-15% 50-75% 75-100%
City of Edinburgh 50-75% 75-100% 75-100% 75-100%
Clackmannanshire 25-50% 50-75% 75-100% 75-100%
Dumfries & Galloway 15-25% 25-50% 50-75% 75-100%
Dundee City 75-100% 75-100% 75-100% 75-100%
East Ayrshire 25-50% 50-75% 75-100% 75-100%
East Dunbartonshire 15-25% 50-75% 75-100% 75-100%
East Lothian 25-50% 50-75% 75-100% 75-100%
East Renfrewshire 5-15% 50-75% 75-100% 75-100%
Falkirk 5-15% 15-25% 50-75% 75-100%
Fife 15-25% 25-50% 75-100% 75-100%
Glasgow City 25-50% 50-75% 75-100% 75-100%
Highland 0-5% 5-15% 15-25% 25-50%
Inverclyde 0-5% 5-15% 50-75% 75-100%
Midlothian 25-50% 50-75% 75-100% 75-100%
Moray 0-5% 0-5% 0-5% 15-25%
Na h-Eileanan Siar 0-5% 0-5% 0-5% 5-15%
North Ayrshire 15-25% 50-75% 75-100% 75-100%
North Lanarkshire 25-50% 25-50% 75-100% 75-100%
Orkney Islands 0-5% 0-5% 0-5% 0-5%
Perth and Kinross 25-50% 75-100% 75-100% 75-100%
Renfrewshire 15-25% 25-50% 75-100% 75-100%
Scottish Borders 15-25% 25-50% 75-100% 75-100%
Shetland Islands 0-5% 0-5% 0-5% 5-15%
South Ayrshire 50-75% 75-100% 75-100% 75-100%
South Lanarkshire 15-25% 25-50% 75-100% 75-100%
Stirling 0-5% 15-25% 75-100% 75-100%
West Dunbartonshire 25-50% 25-50% 75-100% 75-100%
West Lothian 25-50% 50-75% 75-100% 75-100%

What levels of Covid-19 are indicated by wastewater (WW) data?

Table 2 provides population weighted daily averages for normalised WW Covid-19 levels in the weeks of the 28th May and 4th June, with no estimate for error. This is given in Million gene copies per person, which approximately corresponds to new cases per 100,000 per day. Coverage is given as percentage of LA inhabitants covered by a wastewater Covid‑19 sampling site delivering data during this period[15].

Table 2. Average daily cases per 100k as given by WW data
Local authority (LA) Average daily WW case estimate,
with outliers included
Average daily WW case estimate,
with outliers removed
Coverage[16]
w/b 28th May w/b 4th June w/b 28th May w/b 4th June
Aberdeen City 4.6 9.1 4.6 9.1 80%
Aberdeenshire 2.2 2.9 2.2 2.9 52%
Angus 14.0 24.0 14.0 24.0 56%
Argyll and Bute 5.3 2.6 5.3 2.6 18%
City of Edinburgh 14.1 26.3 14.1 26.3 96%
Clackmannanshire 22.7 29.9 17.8 29.9 92%
Dumfries & Galloway 1.3 0.9 1.3 0.9 33%
Dundee City 17.4 23.9 17.4 23.9 100%
East Ayrshire 10.8 20.2 10.8 20.2 72%
East Dunbartonshire 22.3 18.6 22.3 18.6 99%
East Lothian 12.4 24.4 12.4 24.4 65%
East Renfrewshire 24.3 2.7 24.3 2.7 6%
Falkirk 4.3 6.3 4.3 6.3 69%
Fife 4.4 8.7 4.4 8.7 84%
Glasgow City 24.1 20.8 24.1 20.8 62%
Highland 2.5 2.1 2.5 2.1 38%
Inverclyde 6.7 6.2 6.7 6.2 92%
Midlothian 14.0 29.1 14.0 29.1 88%
Moray 1.4 1.6 1.4 1.6 70%
Na h-Eileanan Siar 0.0 0.0 0.0 0.0 21%
North Ayrshire 6.6 9.7 6.6 9.7 93%
North Lanarkshire 10.8 9.8 10.8 9.8 84%
Orkney Islands 0.0 1.9 0.0 1.9 34%
Perth and Kinross 7.5 14.2 7.5 14.2 45%
Renfrewshire 19.7 10.8 19.7 10.8 45%
Scottish Borders 0.1 0.7 0.1 0.7 38%
Shetland Islands 0.8 0.2 0.8 0.2 29%
South Ayrshire 9.6 20.1 9.6 20.1 88%
South Lanarkshire 12.8 7.6 12.8 7.6 59%
Stirling 3.6 2.9 3.6 2.9 63%
West Dunbartonshire 11.4 10.9 11.4 10.9 98%
West Lothian 6.3 7.9 6.0 7.9 85%

Contact

Email: modellingcoronavirus@gov.scot

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