# Coronavirus (COVID-19): modelling the epidemic (issue no. 80)

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.

## 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 method of producing the medium term projections (figures 10 - 12) 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 begin from the point the published data ends.

There is no prediction 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 prediction 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.

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.

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.

### Which local authorities are likely to experience high levels of Covid-19 in two weeks’ time

Table 1. Probability of local authority areas exceeding thresholds of cases per 100K (12th to 18th December). Data to 29th November.
Probability of exceeding (cases per 100K)
Local Authority (LA) 50 100 300 500
Aberdeen City 75-100% 75-100% 25-50% 0-5%
Aberdeenshire 75-100% 75-100% 5-15% 0-5%
Angus 75-100% 75-100% 25-50% 5-15%
Argyll and Bute 75-100% 75-100% 5-15% 0-5%
City of Edinburgh 75-100% 75-100% 25-50% 5-15%
Clackmannanshire 75-100% 75-100% 25-50% 5-15%
Dumfries & Galloway 75-100% 75-100% 25-50% 5-15%
Dundee City 75-100% 75-100% 15-25% 0-5%
East Ayrshire 75-100% 75-100% 25-50% 15-25%
East Dunbartonshire 75-100% 75-100% 25-50% 15-25%
East Lothian 75-100% 75-100% 25-50% 5-15%
East Renfrewshire 75-100% 75-100% 25-50% 15-25%
Falkirk 75-100% 75-100% 50-75% 15-25%
Fife 75-100% 75-100% 25-50% 0-5%
Glasgow City 75-100% 75-100% 25-50% 15-25%
Highland 75-100% 75-100% 0-5% 0-5%
Inverclyde 75-100% 75-100% 15-25% 5-15%
Midlothian 75-100% 75-100% 15-25% 0-5%
Moray 75-100% 75-100% 15-25% 5-15%
Na h-Eileanan Siar 50-75% 25-50% 0-5% 0-5%
North Ayrshire 75-100% 75-100% 25-50% 5-15%
North Lanarkshire 75-100% 75-100% 25-50% 5-15%
Orkney Islands 25-50% 15-25% 0-5% 0-5%
Perth and Kinross 75-100% 75-100% 15-25% 0-5%
Renfrewshire 75-100% 75-100% 25-50% 15-25%
Scottish Borders 75-100% 75-100% 15-25% 0-5%
Shetland Islands 50-75% 25-50% 5-15% 0-5%
South Ayrshire 75-100% 75-100% 15-25% 0-5%
South Lanarkshire 75-100% 75-100% 25-50% 5-15%
Stirling 75-100% 75-100% 25-50% 5-15%
West Dunbartonshire 75-100% 75-100% 25-50% 5-15%
West Lothian 75-100% 75-100% 25-50% 5-15%

### 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 12th November and 19th 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[14].

Table 2. Average daily cases per 100k as given by WW data [15].
Local authority (LA) w/b 12th November w/b 19th November Coverage
Aberdeen City 110 110 99%
Aberdeenshire 75 76 52%
Angus 91 98 68%
Argyll and Bute 3%
City of Edinburgh 49 76 98%
Clackmannanshire 81 82 92%
Dumfries & Galloway 64 95 39%
Dundee City 65 90 100%
East Ayrshire 67 60 57%
East Dunbartonshire 104 105 99%
East Lothian 50 107 74%
East Renfrewshire 51 64 95%
Falkirk 62 105 96%
Fife 101 87 84%
Glasgow City 78 86 71%
Highland 55 70 44%
Inverclyde 44 57 98%
Midlothian 55 75 88%
Moray 82 84 28%
Na h-Eileanan Siar 0%
North Ayrshire 29 70 93%
North Lanarkshire 83 79 41%
Orkney Islands 135 26 34%
Perth and Kinross 87 95 45%
Renfrewshire 62 61 97%
Scottish Borders 66 51 59%
Shetland Islands 10 41 29%
South Ayrshire 60 63 88%
South Lanarkshire 66 79 83%
Stirling 49 51 63%
West Dunbartonshire 68 76 98%
West Lothian 56 52 95%