It can be hard to keep track of the progress of the epidemic as the daily cases, hospitalisations and deaths often seem to tell a contradictory story. Each suffers from random noise, delays and incompleteness in reporting, and arguments about how exactly they should be compiled. However, the total number of Covid-19 patients in hospital in the north-west has recently been growing in a disturbingly consistent way – and justifies the strict new rules which have been brought in today in the region.
On 26 August, the number of hospitalised Covid patients in the region reached a low of 77. Five weeks later, this number has grown to 612 – an eightfold increase. While this is much lower than the 2,890 reached on 13 April, another eightfold increase would see it far exceed that first-wave peak. The arithmetic of epidemic growth means that such a further increase, perhaps over a similar timescale, cannot be ruled out – and could even be regarded as the expected outcome. Given constraints on NHS capacity, heightened by regular winter flu admissions, I believe this is a risk we need to take seriously.
I have described the situation in terms of multiplicative (‘eightfold’) changes, which may seem curious. However, this is the right way to think about the spread of the virus. Without intervention we can expect that on average each infected individual will infect the same number of people – the famous R number. If this value is greater than 1, the number of infections will grow by a comparable percentage each day and, as I have described before, the size of the epidemic will appear as a straight line on a logarithmic graph. This is exactly the behaviour that I have observed for the north-west hospital data, which is why I am worried.
Of course, many famous predictions based on uncontrolled exponential growth have failed to come true. Growth of an epidemic can be checked by many effects, including widespread vaccinations or increasing levels of antibody immunity in the population. However, my view is that it is extremely optimistic to believe that either of those will slow the current spread in the north west in time. The most likely scenario for a flattening of the curve seems to come through further reductions in social contacts – although this exponential growth in patients has taken place despite wide-ranging local lockdowns since the summer.
This does not necessarily mean a full lockdown, with associated economic and social costs, will be necessary. The Rule of Six, curfews and increased working from home may yet do enough, though any immediate changes will take a while to have an effect. However, I believe that the precautionary principle suggests that we need to take exponential growth scenarios seriously, and urgently plan to mitigate them. The experiences of Lombardy and New York City in March and April are a reminder of the grave dangers of regional health resources becoming overwhelmed, and mean that we should all be keeping an eye on these numbers, for the north west and beyond.
Oliver Johnson is a professor of information theory and the director of the Institute for Statistical Science at the University of Bristol