# Coronavirus (COVID-19): modelling the epidemic (issue no. 59)

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 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 midâ€‘January onward. During mid-December to mid-January, 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, after which they include people in ICU over the 28 day limit.

### How is wastewater data used in our modelling?

The Scottish Government has historically used either deaths or cases, as published by Public Health Scotland (PHS), to inform its model to estimate current R values, incidence figures and growth rates.

In recent months, these research findings have explained how an estimate of cases can be made by examining the levels of Covid-19 RNA in wastewater, collected throughout Scotland and adjusted for population and local changes in intake flow rate.

We have developed our modelling such that it is possible to calculate the main nowcast outputs by using this wastewater data, instead of the case data from PHS.

The Scottish WW data is population weighted averages for normalised Wastewater Covid levels. The units are provided in 1 million gene copies per person per day, which roughly matches with cases per 100,000 per day. This is converted into daily cases at a national level. The model makes an allowance for the proportion of infections which are positively identified as cases (using a comparison with the ONS Covid Infection Survey[13]), and then uses a Bayesian method to estimate the key variables throughout the pandemic.

We are currently only using the wastewater data for Scottish cases, but are working with colleagues in the other UK nations to use their wastewater data in a similar way.

Table 1. Probability of local authority areas exceeding thresholds of cases per 100K (18th to 24th July 2021), data to 5th July.
Probability of exceeding (cases per 100k)
LA 20 50 100 150 300 500 750 1000 2000
Aberdeen City 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 5-15%
Aberdeenshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 5-15% 0-5%
Angus 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 25-50% 0-5%
Argyll and Bute 75-100% 50-75% 50-75% 50-75% 25-50% 25-50% 0-5% 0-5% 0-5%
City of Edinburgh 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 50-75% 15-25%
Clackmannanshire 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 5-15% 0-5% 0-5%
Dumfries & Galloway 75-100% 75-100% 75-100% 75-100% 25-50% 5-15% 5-15% 0-5% 0-5%
Dundee City 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50%
East Ayrshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 15-25% 0-5%
East Dunbartonshire 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 5-15%
East Lothian 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 25-50% 25-50% 0-5%
East Renfrewshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 25-50% 5-15%
Falkirk 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 15-25% 0-5%
Fife 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 25-50%
Glasgow City 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 25-50% 15-25%
Highland 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 50-75% 25-50% 5-15%
Inverclyde 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 25-50% 25-50% 0-5%
Midlothian 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 25-50% 5-15%
Moray 75-100% 75-100% 50-75% 50-75% 15-25% 5-15% 5-15% 0-5% 0-5%
Na h-Eileanan Siar 25-50% 15-25% 5-15% 0-5% 0-5% 0-5% 0-5% 0-5% 0-5%
North Ayrshire 75-100% 75-100% 75-100% 75-100% 75-100% 25-50% 15-25% 5-15% 0-5%
North Lanarkshire 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 5-15%
Orkney Islands 25-50% 25-50% 15-25% 5-15% 0-5% 0-5% 0-5% 0-5% 0-5%
Perth and Kinross 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 15-25%
Renfrewshire 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 5-15%
Scottish Borders 75-100% 75-100% 50-75% 50-75% 25-50% 25-50% 15-25% 0-5% 0-5%
Shetland Islands 25-50% 15-25% 5-15% 0-5% 0-5% 0-5% 0-5% 0-5% 0-5%
South Ayrshire 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 15-25% 5-15% 0-5%
South Lanarkshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 25-50% 5-15%
Stirling 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 15-25% 5-15% 0-5%
West Dunbartonshire 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 50-75% 25-50% 0-5%
West Lothian 75-100% 75-100% 75-100% 75-100% 75-100% 75-100% 50-75% 25-50% 5-15%

### 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 the 19th June and 26th 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 Covidâ€‘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 19th June w/b 26th June w/b 19th June w/b 26th June
Aberdeen City 46.0 85.0 46.0 85.0 80%
Aberdeenshire 14.0 29.0 14.0 29.0 53%
Angus 49.0 59.0 49.0 59.0 56%
Argyll and Bute 0.0 3.0 0.0 3.0 18%
City of Edinburgh 30.0 144.0 30.0 144.0 97%
Clackmannanshire 32.0 32.0 32.0 32.0 92%
Dumfries & Galloway 8.0 26.0 8.0 26.0 32%
Dundee City 60.0 72.0 60.0 72.0 100%
East Ayrshire 34.0 30.0 34.0 30.0 72%
East Dunbartonshire 42.0 83.0 42.0 83.0 0%
East Lothian 28.0 130.0 28.0 130.0 65%
East Renfrewshire 33.0 62.0 33.0 62.0 95%
Falkirk 13.0 62.0 13.0 62.0 69%
Fife 31.0 74.0 31.0 74.0 80%
Glasgow City 37.0 70.0 37.0 70.0 63%
Highland 12.0 31.0 12.0 31.0 36%
Inverclyde 18.0 46.0 18.0 46.0 93%
Midlothian 31.0 138.0 31.0 138.0 88%
Moray 4.0 18.0 4.0 2.0 56%
Na h-Eileanan Siar 0.0 0.0 0.0 0.0 21%
North Ayrshire 24.0 23.0 24.0 23.0 93%
North Lanarkshire 26.0 35.0 26.0 35.0 77%
Orkney Islands 11.0 4.0 11.0 4.0 34%
Perth and Kinross 20.0 29.0 20.0 29.0 45%
Renfrewshire 20.0 44.0 20.0 44.0 57%
Scottish Borders 21.0 13.0 21.0 11.0 49%
Shetland Islands 0.0 0.0 0.0 0.0 29%
South Ayrshire 35.0 23.0 35.0 23.0 88%
South Lanarkshire 23.0 53.0 23.0 53.0 87%
Stirling 8.0 27.0 3.0 27.0 63%
West Dunbartonshire 24.0 11.0 24.0 11.0 50%
West Lothian 24.0 35.0 24.0 35.0 78%