Publication - Research and analysis

Coronavirus (COVID-19): modelling the epidemic (issue no.78)

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.78)
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

Since last week, the method of producing the medium term projections (figures 10 - 12) has been updated. The update uses the published actual numbers of infections, hospital admissions and ICU admissions directly, rather than modelling them from the beginning of the epidemic. This means the projections now begin from the point the published data ends.

There is no longer a confidence interval around the actual infections in Figure 10 because there is no longer any uncertainty from simulating infections during this period. There is still uncertainty in the ascertainment rate, which is represented by the whiskers around the actual infections.

The confidence intervals around the actual hospital and ICU occupancy in figures 11 and 12 now represent uncertainty in the assumptions for the hospitalisation rate and hospital length of stay, rather than uncertainty in the number of infections. These confidence intervals are created by applying sensitivity analysis to the assumptions.

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 (21st to 27th November 2021), data to 8th November.
Probability of exceeding (cases per 100K)
Local Authority (LA) 50 100 300 500
Aberdeen City 75-100% 75-100% 50-75% 25-50%
Aberdeenshire 75-100% 75-100% 50-75% 15-25%
Angus 75-100% 75-100% 75-100% 50-75%
Argyll and Bute 75-100% 75-100% 50-75% 15-25%
City of Edinburgh 75-100% 75-100% 50-75% 15-25%
Clackmannanshire 75-100% 75-100% 75-100% 50-75%
Dumfries & Galloway 75-100% 75-100% 75-100% 50-75%
Dundee City 75-100% 75-100% 25-50% 5-15%
East Ayrshire 75-100% 75-100% 75-100% 50-75%
East Dunbartonshire 75-100% 75-100% 75-100% 25-50%
East Lothian 75-100% 75-100% 50-75% 25-50%
East Renfrewshire 75-100% 75-100% 75-100% 25-50%
Falkirk 75-100% 75-100% 75-100% 50-75%
Fife 75-100% 75-100% 75-100% 25-50%
Glasgow City 75-100% 75-100% 25-50% 25-50%
Highland 75-100% 75-100% 50-75% 50-75%
Inverclyde 75-100% 75-100% 50-75% 15-25%
Midlothian 75-100% 75-100% 50-75% 15-25%
Moray 75-100% 75-100% 50-75% 50-75%
Na h-Eileanan Siar[12] - - - -
North Ayrshire 75-100% 75-100% 50-75% 15-25%
North Lanarkshire 75-100% 75-100% 50-75% 25-50%
Orkney Islands12 - - - -
Perth and Kinross 75-100% 75-100% 50-75% 50-75%
Renfrewshire 75-100% 75-100% 50-75% 15-25%
Scottish Borders 75-100% 75-100% 50-75% 25-50%
Shetland Islands12 - - - -
South Ayrshire 75-100% 75-100% 75-100% 25-50%
South Lanarkshire 75-100% 75-100% 75-100% 25-50%
Stirling 75-100% 75-100% 50-75% 25-50%
West Dunbartonshire 75-100% 75-100% 50-75% 5-15%
West Lothian 75-100% 75-100% 50-75% 15-25%

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 2nd November and 9th November 2021, 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[13].

Table 2. Average daily cases per 100k as given by WW data [14].
Local authority (LA) w/b 2nd November w/b 9th November Coverage
Aberdeen City 97.8 81 99%
Aberdeenshire 70.8 48 52%
Angus 39.0 56 68%
Argyll and Bute 3%
City of Edinburgh 53.4 34 98%
Clackmannanshire 89.2 105 92%
Dumfries & Galloway 62.8 76 38%
Dundee City 29.8 62 100%
East Ayrshire 131.2 50 57%
East Dunbartonshire 60.6 89 99%
East Lothian 51.5 39 74%
East Renfrewshire 58.0 45 95%
Falkirk 58.5 47 95%
Fife 56.6 88 84%
Glasgow City 55.9 64 75%
Highland 26.1 44 37%
Inverclyde 59.2 34 98%
Midlothian 52.2 37 88%
Moray 42.6 47 14%
Na h-Eileanan Siar 0%
North Ayrshire 36.1 32 93%
North Lanarkshire 40.8 40 91%
Orkney Islands 18.2 40 34%
Perth and Kinross 84.7 80 45%
Renfrewshire 46.8 50 97%
Scottish Borders 45.5 63 59%
Shetland Islands 0.6 0%
South Ayrshire 60.0 55 88%
South Lanarkshire 57.6 61 82%
Stirling 25.1 24 63%
West Dunbartonshire 59.5 60 98%
West Lothian 79.5 52 87%

Contact

Email: modellingcoronavirus@gov.scot