Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 68)

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. 68)
Technical Annex

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.

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 20. Infections projections versus actuals, for historical projections published between one and two weeks before the actual data came in.

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 21. Hospital bed projections versus actuals, for historical projections published between one and two weeks before the actual data came in.

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 22. ICU bed projections versus actuals, for historical projections published between one and two weeks before the actual data came in.

A combination line and scatter graph comparing ICU occupancy projections against actuals.

Table 1. Probability of local authority areas exceeding thresholds of cases per 100K (19th to 25th September 2021), data to 6th September.
Probability of exceeding (cases per 100k)
Local Authority (LA) 50 100 300 500 1000 1500
Aberdeen City 75-100% 75-100% 75-100% 75-100% 25-50% 5-15%
Aberdeenshire 75-100% 75-100% 75-100% 75-100% 25-50% 15-25%
Angus 75-100% 75-100% 75-100% 50-75% 15-25% 15-25%
Argyll and Bute 75-100% 75-100% 75-100% 50-75% 50-75% 15-25%
City of Edinburgh 75-100% 75-100% 75-100% 75-100% 50-75% 25-50%
Clackmannanshire 75-100% 75-100% 75-100% 50-75% 50-75% 25-50%
Dumfries & Galloway 75-100% 75-100% 75-100% 50-75% 25-50% 0-5%
Dundee City 75-100% 75-100% 75-100% 75-100% 25-50% 15-25%
East Ayrshire 75-100% 75-100% 75-100% 75-100% 50-75% 15-25%
East Dunbartonshire 75-100% 75-100% 75-100% 75-100% 25-50% 25-50%
East Lothian 75-100% 75-100% 75-100% 50-75% 15-25% 5-15%
East Renfrewshire 75-100% 75-100% 75-100% 75-100% 50-75% 25-50%
Falkirk 75-100% 75-100% 75-100% 75-100% 50-75% 15-25%
Fife 75-100% 75-100% 75-100% 75-100% 75-100% 25-50%
Glasgow City 75-100% 75-100% 75-100% 75-100% 75-100% 50-75%
Highland 75-100% 75-100% 75-100% 75-100% 25-50% 15-25%
Inverclyde 75-100% 75-100% 75-100% 50-75% 50-75% 25-50%
Midlothian 75-100% 75-100% 75-100% 50-75% 25-50% 15-25%
Moray 75-100% 50-75% 50-75% 25-50% 5-15% 5-15%
Na h-Eileanan Siar 25-50% 25-50% 25-50% 15-25% 0-5% 0-5%
North Ayrshire 75-100% 75-100% 75-100% 75-100% 50-75% 15-25%
North Lanarkshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75%
Orkney Islands 25-50% 15-25% 0-5% 0-5% 0-5% 0-5%
Perth and Kinross 75-100% 75-100% 75-100% 25-50% 5-15% 0-5%
Renfrewshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75%
Scottish Borders 75-100% 75-100% 75-100% 50-75% 5-15% 0-5%
Shetland Islands 25-50% 25-50% 25-50% 25-50% 0-5% 0-5%
South Ayrshire 75-100% 75-100% 75-100% 75-100% 25-50% 5-15%
South Lanarkshire 75-100% 75-100% 75-100% 75-100% 50-75% 50-75%
Stirling 75-100% 75-100% 75-100% 50-75% 25-50% 5-15%
West Dunbartonshire 75-100% 75-100% 75-100% 75-100% 50-75% 25-50%
West Lothian 75-100% 75-100% 75-100% 75-100% 50-75% 15-25%

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 beginning 21st and 28th August, 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[12].

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[13]
w/b 21st August w/b 28th August w/b 21st August w/b 28th August
Aberdeen City 88 150 88 150 80 %
Aberdeenshire 62 131 56 127 50 %
Angus 84 196 84 196 56 %
Argyll and Bute -- -- -- -- 3 %
City of Edinburgh 97 123 97 123 96 %
Clackmannanshire 183 192 183 192 92 %
Dumfries & Galloway 103 97 103 97 36 %
Dundee City 96 237 96 237 100 %
East Ayrshire 122 234 122 234 72 %
East Dunbartonshire 107 249 107 249 99 %
East Lothian 92 124 92 124 65 %
East Renfrewshire 161 232 161 232 95 %
Falkirk 58 131 58 131 69 %
Fife 108 130 108 124 52 %
Glasgow City 131 267 131 267 98 %
Highland 92 141 92 141 37 %
Inverclyde 48 89 48 89 92 %
Midlothian 114 142 114 142 88 %
Moray 23 52 23 52 70 %
Na h-Eileanan Siar 40 5 -- 5 21 %
North Ayrshire 90 116 90 116 93 %
North Lanarkshire 123 151 123 151 91 %
Orkney Islands 11 12 11 12 34 %
Perth and Kinross -- 144 -- 68 44 %
Renfrewshire 156 348 156 348 57 %
Scottish Borders 108 62 110 56 56 %
Shetland Islands 1 1 1 1 29 %
South Ayrshire 122 265 122 265 82 %
South Lanarkshire 199 279 199 279 82 %
Stirling 35 16 35 16 63 %
West Dunbartonshire 107 126 107 126 98 %
West Lothian -- 131 -- 131 85 %

Contact

Email: modellingcoronavirus@gov.scot