Mathematical models simulated vast numbers of possible futures for after the UK government lifts Covid restrictions in England from 19 July. Many sources of uncertainty mean we don’t know which one, if any, of these projections might occur.
First, even with fixed assumptions about the epidemic, the play of chance produces wide prediction intervals. For example, assuming people substantially relax their cautious behaviour after 19 July, the Warwick models lead to peak Covid hospital admissions of 900 to 3,000 a day around the end of August.
Second, there is uncertainty about the assumptions, leading to extremely complex sensitivity analyses. Warwick has a default assumption that two doses of the Oxford-AstraZeneca vaccine is 94% effective against hospital admission, compared with an “optimistic” 97% and a “cautious” 90%. These differences may not seem large, but perhaps it is better to think of 94% effectiveness as 6% ineffectiveness. This means the optimistic assumption of 3% ineffectiveness will roughly halve the number of admissions compared with the default. Similarly, 90% vaccine coverage means twice as many unvaccinated people as an uptake of 95%, with serious impacts. Such “re-framing” usually goes the other way, when a potentially worrying 2% mortality rate from surgery can be turned into a more reassuring 98% survival rate.
The way people behave after restrictions are lifted will also have huge effects: a reproduction number of 1.2 may sound similar to 1.4, but after four viral generations new infections will be about 85% higher under the latter epidemic.
The appropriate mathematical structure of the model is also uncertain, so it is good to have independent teams. Imperial’s model has higher estimated admissions than Warwick and the London School of Hygiene & Tropical Medicine, projecting a peak of Covid hospital admissions of around 5,000 a day under high efficacy. A final source of uncertainty comes from all models being inadequate: events may happen outside what the model can describe.
The Sage modelling sub-group notes: “All results are highly sensitive to the modelling assumptions, and extensive sensitivity analyses have been performed.” We can be certain of an exit wave, but not about its scale and duration.
• David Spiegelhalter is chair of the Winton Centre for Risk and Evidence Communication at Cambridge. Anthony Masters is statistical ambassador for the Royal Statistical Society
