Being able to predict and estimate how a disease might behave is crucial in the fight against large-scale pandemics such as COVID-19. As economists, we are more used to modelling and forecasting growth in the economy. But when the COVID-19 pandemic unfolded we thought we could help, since there are clear parallels between forecasting the behaviour of the economy and the spread of an epidemic. So we used the same skills and tools we use in economic and financial analysis to look at the timeline of COVID-19. We have developed models to track and predict the numbers of infections and deaths and are now using them to publish daily short-term forecasts of coronavirus UK mortality rates, available here.
These models were initially designed to detect so-called turning points, which occur for example when an economy moves from recession to recovery, or when the number of new infections or deaths caused by a disease begins to fall. They clearly indicate that the peak in the daily death toll in the UK occurred on 8 April and that the mortality figures are now trending down — easing the pressure on the NHS and its staff. Our initial results are described in a departmental Discussion Paper.
We initially concentrated on the headline UK announcements of infections and hospital deaths. However, in view of the long delays in reporting deaths from the virus, we then switched our focus to figures released by NHS England that show mortality on a date-of-death rather than date-of-announcement basis. This model gives predictions that allow for deaths that have probably already occurred but not been announced. It is currently suggesting that 19,000 people will die from the virus in English hospitals by the end of April. On current trends, the UK figure is likely to be 10% higher. After that, the impact of the virus will depend critically upon the government’s plan for relaxing its current strategy of suppression.
So many forecasts – how much weight should we give to them?
Estimates of the effects of COVID-19 seem to vary massively. In the middle of March 2020, for example, one study predicted that the UK would have 5,800 deaths from COVID-19. Another report from the University of Washington’s Institute for Health Metrics and Evaluation has predicted that the UK will have more than 66,300 deaths from COVID-19. This range of estimates reflects the great uncertainty still surrounding COVID-19 – and that so much is still unknown about its behaviour. It also illustrates the fact that there are many different ways of analysing the progress of an epidemic.
The UK government and its advisers mainly rely upon large computer models that analyse the likely spread of the disease and the effects of public health interventions such as lockdown, as this report illustrates. Whereas, the charts shown on the news, showing the cumulative numbers of hospital admissions, use the experience of countries that were hit earlier to judge what is likely to happen in other countries.
Other epidemiologists fit so-called logistic curves to these figures to predict the probability of a certain number of deaths. This simple curve fitting approach accurately predicted the evolution of the COVID-19 outbreak in Wuhan, China. These S shaped curves bend upwards to capture the initial phase of rapid exponential growth and then gradually flatten out as the epidemic slows and eventually peters out.
However, fitting curves to series that can grow exponentially is problematic, because shocks to the system have an explosive effect going forward. Economists and biologists have developed statistical techniques for handling this problem. So, instead of fitting a logistic curve to the cumulative death figures, we deal with this problem using an equation that represents the mortality rate and relates this to the number of new daily cases.
How our model works
The equation is based on what is known as the S-I-R disease model. This sees infections as the result of random encounters between so-called susceptible people – who have not yet had the disease – and infectious people – that are still contagious but not isolated. The rest of the population are considered to have already had the infection and are called the “removed class”. These are the people who have either recovered and are assumed immune, or who have sadly died.
The initial spread of the disease is rapid because most people are susceptible, but then moderates and eventually dies out as the number that are susceptible falls. A similar deceleration occurs as people see the number of cases increasing and become more cautious. Our research suggests that this behavioural change has been very important in helping to reduce the spread in many countries, including the UK.
Small is beautiful
The beauty of our model is that it can be easily updated as new data arrives. It can distinguish the trend from misleading day-to-day movements and then use this to identify turning points. It provides estimates of the uncertainty that must surround any forecast, especially at the moment.
That said, it is difficult to use our model to predict the effect of government interventions, since these only reveal themselves to us afterwards as the long range estimates of the death toll begin to fall. However, these simple models complement the big models well. Indeed, the economics profession has long recognised that ‘it’s a matter of horses for courses’.
For example, Bank of England economists have a suite of economic models that they use for different tasks, ranging from large theory-based models for simulating the effects of policy changes to smaller data-based models used to make short-term forecasts and to support the decisions of the Monetary Policy Committee. Again, the parallel between epidemic and economic modelling is very clear.