Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no. 71)

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. 71)
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 2020 and from mid‑January 2021 onwards. During mid-December 2020 to mid‑January 2021, the projections underestimated the number of infections, due to the unforeseen effects of the new variant.

Figure 19. 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 20. 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 2021, after which they include people in ICU over the 28 day limit.

Figure 21. 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 (10th to 16th October 2021), data to 27th September.
Probability of exceeding (cases per 100k)
Local Authority (LA) 50 100 300 500 750 1000
Aberdeen City 75-100% 75-100% 50-75% 15-25% 5-15% 0-5%
Aberdeenshire 75-100% 75-100% 50-75% 15-25% 0-5% 0-5%
Angus 75-100% 75-100% 15-25% 0-5% 0-5% 0-5%
Argyll and Bute 75-100% 75-100% 25-50% 0-5% 0-5% 0-5%
City of Edinburgh 75-100% 75-100% 25-50% 25-50% 15-25% 5-15%
Clackmannanshire 75-100% 75-100% 50-75% 25-50% 5-15% 0-5%
Dumfries & Galloway 75-100% 75-100% 50-75% 5-15% 0-5% 0-5%
Dundee City 75-100% 75-100% 75-100% 25-50% 15-25% 5-15%
East Ayrshire 75-100% 75-100% 75-100% 50-75% 25-50% 5-15%
East Dunbartonshire 75-100% 75-100% 50-75% 25-50% 5-15% 0-5%
East Lothian 75-100% 50-75% 5-15% 0-5% 0-5% 0-5%
East Renfrewshire 75-100% 75-100% 25-50% 5-15% 0-5% 0-5%
Falkirk 75-100% 75-100% 50-75% 15-25% 0-5% 0-5%
Fife 75-100% 75-100% 75-100% 25-50% 15-25% 5-15%
Glasgow City 75-100% 75-100% 75-100% 25-50% 25-50% 25-50%
Highland 75-100% 50-75% 0-5% 0-5% 0-5% 0-5%
Inverclyde 75-100% 75-100% 25-50% 0-5% 0-5% 0-5%
Midlothian 75-100% 75-100% 25-50% 0-5% 0-5% 0-5%
Moray 75-100% 50-75% 15-25% 5-15% 0-5% 0-5%
Na h-Eileanan Siar 25-50% 25-50% 5-15% 0-5% 0-5% 0-5%
North Ayrshire 75-100% 75-100% 50-75% 25-50% 0-5% 0-5%
North Lanarkshire 75-100% 75-100% 75-100% 50-75% 25-50% 15-25%
Orkney Islands 25-50% 5-15% 0-5% 0-5% 0-5% 0-5%
Perth and Kinross 75-100% 75-100% 50-75% 25-50% 5-15% 0-5%
Renfrewshire 75-100% 75-100% 50-75% 15-25% 5-15% 0-5%
Scottish Borders 75-100% 50-75% 0-5% 0-5% 0-5% 0-5%
Shetland Islands 15-25% 5-15% 0-5% 0-5% 0-5% 0-5%
South Ayrshire 75-100% 75-100% 75-100% 50-75% 25-50% 5-15%
South Lanarkshire 75-100% 75-100% 75-100% 25-50% 15-25% 5-15%
Stirling 75-100% 75-100% 25-50% 5-15% 0-5% 0-5%
West Dunbartonshire 75-100% 75-100% 50-75% 25-50% 0-5% 0-5%
West Lothian 75-100% 75-100% 75-100% 25-50% 5-15% 0-5%

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

Table 2 provides population weighted daily averages for normalised WW Covid-19 levels in the weeks beginning 15th and 22nd September, 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[14].

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[15]
w/b 15th September w/b 22nd September w/b 15th September w/b 22nd September
Aberdeen City 36 44 36 44 80%
Aberdeenshire 50 40 50 40 18%
Angus 125 85 125 85 43%
Argyll and Bute 0%
City of Edinburgh 87 82 87 82 96%
Clackmannanshire 71 71 0%
Dumfries & Galloway 35 92 35 92 29%
Dundee City 139 85 139 85 100%
East Ayrshire 70 150 70 150 57%
East Dunbartonshire 78 78 99%
East Lothian 87 73 87 73 65%
East Renfrewshire 136 73 136 73 89%
Falkirk 93 39 93 39 59%
Fife 104 65 104 65 48%
Glasgow City 141 83 141 83 98%
Highland 71 71 71 71 31%
Inverclyde 59 56 59 56 92%
Midlothian 100 86 100 86 88%
Moray 33 33 0%
Na h-Eileanan Siar 10 46 10 46 21%
North Ayrshire 45 63 45 63 92%
North Lanarkshire 183 92 183 92 88%
Orkney Islands 17 16 17 16 34%
Perth and Kinross 107 152 107 152 38%
Renfrewshire 120 38 120 38 57%
Scottish Borders 18 22 18 22 46%
Shetland Islands 6 3 6 3 29%
South Ayrshire 41 145 41 145 84%
South Lanarkshire 126 129 126 129 64%
Stirling 21 21 63%
West Dunbartonshire 5 78 5 78 48%
West Lothian 129 97 129 97 64%

Contact

Email: modellingcoronavirus@gov.scot