Tread carefully when predicting fatality rates

We experience the world through our senses, and strive to build our understanding by constructing some kind of replica in our minds of what is actually out there.

Mathematical modelling is an extension of this fundamental activity. The Covid-19 pandemic has, at its heart, a very simple dynamic which can be captured by the fundamental SIR model, known as a powerful tool for dissecting the spread of diseases which have short “infectious” periods and where “recovery” renders an individual unavailable for infection.

Members of a population can be allocated to the “I” and “R” bins, with the remainder being left in the “susceptible” bin; hence SIR.

The behaviour of these SIR systems is fully specified by two factors: how long an individual is infectious, and the fundamental transmission potential of the pathogen. Fortunately, both of these can be estimated at a fairly early stage of the epidemic. What is harder to estimate at the early stage is the infection fatality rate.

Two extreme scenarios fit the data. In one, as assumed by the Imperial College modellers, the fatality rate is in the ball park of 1pc, which would imply the epidemic took off towards the end of February in the UK and less than 10pc of the population had been exposed by time of lockdown. In the other, the fatality rate could be as low as 0.01pc. This would require the virus to have been introduced about a month earlier and for over 50pc of individuals to be exposed by March 23.

In essence, the Covid-19 situation is one that can be served by the canonical SIR model. Elaborate computer models could be used to simulate specific activities such as standing two metres apart in a queue but this is contingent on the validity of the underlying assumptions.

Simple models induce you to consider a range of possibilities of the key parameters, while complicated models tend to “fit” parameters to the available data. Most modellers have fitted their models to very limited data available at the time of lockdown on cases and deaths as reported. This corresponds to a particular solution of the general SIR model with a high fatality rate – the worst-case scenario.

But how plausible is a fatality rate of 1pc? A more robust approach would be to measure the proportion already exposed to the virus. The rapid refinement of antibody detection methods over the last couple of months will enable this, allowing us to determine the true fatality rate.

Sunetra Gupta is a professor of theoretical epidemiology at the University of Oxford