Coronavirus (COVID-19): modelling the epidemic

How Covid-19 is modelled

There are two types of modelling which are done to help us respond to Covid-19. The first type of modelling is about the Covid-19 epidemic. This is called "epidemiological" modelling. The second type of modelling uses the first type to help plan our response to Covid-19 in Scotland. This is called "logistics" modelling.

Epidemiological Modelling

There are a range of academic groups doing epidemiological modelling of Covid-19. These academic groups feed in their results to a group at a UK level called the "Scientific Pandemic Influenza Group on Modelling (SPI-M)". Scottish Government uses the modelling from this group along with its own modelling (using a publically available Imperial College modelling code) to advise on the potential future progression of the Covid-19 epidemic in Scotland e.g. in terms of the reproduction rate R and what might happen if we ease lockdown.

The SPI-M group feeds its modelling expertise to the UK Scientific Advisory Group for Emergencies (SAGE) which gives advice on Covid-19 to governments across the UK. In Scotland this is through the Scottish Government COVID-19 Advisory Group which considers this advice and potential impacts in Scotland.

There are a number of groups who are modelling the Covid-19 epidemic in the general population in Scotland, including:

• London School of Hygiene and Tropical Medicine
• University of Warwick
• University of Manchester
• Scottish Government (using the publically available Imperial College Modelling Code)

Scottish Government (using the publically available Imperial College Modelling Code)

Scottish Government uses the publically available Imperial model as reported in their Report 13 to help understand the Covid-19 epidemic in Scotland over the longer term and what the reproductive rate at a point in time (R_t) is for Scotland. The model is run with full settings as recommended by Imperial College^[1].

The model is modified by removing the UK entry in the list of European countries and replacing with England, Scotland, Wales and Northern Ireland as separate nations. Sensitivity analysis has not been undertaken to assess how this alters the sampling behaviour with the additional countries and data series. It may result to differences in the outputs to the Imperial College model reported values for other countries. Smaller nations which are similar to Scotland are included in the model (for example Denmark or Norway), and although sampling will likely be driven by larger populations, it appears to have not skewed the results for these nations.

The intervention dates (e.g. when lockdown started) used are those relevant to the country in question. The infection fatality ratio (IFR), which is the proportion of people infected with Covid-19 that die (based on each countries age structure - Scotland's population for example contains a greater proportion of older people than the UK as a whole), are taken from the IFR value for the UK published by Imperial College London, apportioning population share of each nation and scaling based on the paper from the University of St Andrews for age corrected IFR for UK nations^[2]. Data on cases and deaths come from a range of publically available sources^[3].

The model estimates, within intervals of uncertainty, the number of infections, number of deaths and the reproductive rate of the virus at a point in time (R_t) based on the time series of cases, in the same manner as the Imperial report. Imperial College is not involved in running the model. Scottish Government does this as Imperial College runs their models for the UK as a whole, not for individual UK nations. There are, however, other academic groups who model Scotland (see above). Their modelling is also used to help Scotland plan its response to the Covid-19 epidemic.

Short and long term forecasts

There are short term forecasts of Covid-19 (over the next two weeks) and long term modelling of Covid-19 (over the next couple of months). Short term modelling helps us understand what the NHS needs to plan for nationally in the next two week period while longer term modelling helps us to look at what is happening in regard to the progression of the epidemic. As we go further into the future, what might happen becomes less certain.

The modelling is updated every week. Longer term modelling is currently updated over each weekend based on the best data available from the previous week. By comparing the different models we are able to say with more confidence what might happen. For the short term, models from different groups are used together to give a combined two week forecast. For the longer term modelling different models are compared to see if results are similar. The Scottish Government modelling using the Imperial College public code each week is compared to the other models to add confidence in the results.

There are also a range of subgroups of SAGE and SPI-M looking at different aspects of Covid-19 e.g. on Covid-19 in care homes and other situations around Covid-19 which also feed information into the different governments of the UK including Scotland.

Logistical Modelling

Logistics modelling is undertaken by each government in the UK for use by their key public sector partners e.g. Health Boards to help plan their response.

Modellers from the four countries governments across the UK meet regularly to talk through their logistics modelling and to share best practice.

Logistics modelling in Scotland produces forecasts for the next few months, using the epidemiological modelling based on the Imperial Modelling Code run by Scottish Government. Amongst other things, it gives the "most likely" number of Covid-19 cases needing hospitalisation or an ICU bed. It also gives upper and lower bounds of confidence. These mark the levels at which the model estimates there is a 2.5% chance of the level being above (upper bound), or below (lower bound). The upper bound is labelled as a "worse" scenario and the lower bound labelled as "better".