Whilst both the UK and the US can be said to have been
slow in initiating forceful measures to deal with the Coronavirus epidemics in
their countries, the UK government under Prime Minister Boris Johnson has now,
albeit not always with the necessary clarity, announced shutdowns of most
social-mixing in Britain. Only ‘essential workers’ – a term yet to be
satisfactorily defined – should be leaving their homes except for shopping for
necessary goods, healthcare access or for suitably distancing exercise. There
are problems in obtaining adequate protective equipment for front-line health-workers,
but central government do seem to be making some effort to address this.
Unfortunately, in the US, the leadership vacuum in the
shape of Donald Trump is more interested in spreading misinformation and
bigging-up his own desultory (frankly negative) role in efforts to combat the virus
and its consequences. Any effective efforts to counsel isolation of those with
symptoms and general social-distancing, and to provide additional equipment and
space in anticipation of the inevitable rise in the number of cases needing
hospitalisation, have been taken by State governors, and mainly Democratic
ones. Worse still, Trump is now touting the idea that ‘the cure is worse than
the disease’ and that such restrictions as there are should be relaxed after another
two weeks to allow business (and from his point of view the stock market) to recover.
Apart from the fact that cases and deaths will almost certainly still be rising
at that time, the degree of complacency this signals is likely to be extremely
damaging to ongoing suppression efforts in the United States.
These different approaches by the executives in the two countries are paralleled by the tracks of the case and death growth rates, although it is impossible to say at this stage whether there is any causal relation. Be that as it may, there is some evidence that the UK growth curves are beginning to slope a little more shallowly, while the slopes of the US curves are static at best (Chart 1). The track of the 5-day average growth rates confirms this, particularly when it comes to the growth rate in deaths which with variable testing regimes is probably a better guide to progress, with the UK growth rate at 21.5% now falling below that of the US at 27% (Chart 2).
In addition, even if all patients were able to be treated, we predict [under a mitigation strategy] there would still be in the order of 250,000 deaths in GB, and 1.1-1.2 million in the US. In the UK, this conclusion has only been reached in the last few days, with the refinement of estimates of likely ICU demand due to COVID-19 based on experience in Italy and the UK (previous planning estimates assumed half the demand now estimated) and with the NHS providing increasing certainty around the limits of hospital surge capacity.
Yet, as I described in my previous post, a figure in the
region of 250,000 deaths could have been reached by somewhat simpler calculation.
There is little sign of any alteration to the trajectory I
outlined previously. The UK growth in cases over the last 7 days averages at
around 0.25, whereas that in the US is close to 0.3. This means that new confirmed
cases each day in the UK are around a quarter of the total cases from the day
before, but in the US this is closer to one third. These differences may
represent policy changes in each country, with the UK restricting testing to
hospitalised cases, and the US attempting to ramp up testing from its previous relatively
low level. We can project these rates of growth into the future however to
suggest that the UK will have reached 10,000 cases in around five days, and the
US 100,000 cases in about 1 week (Chart
1). Over the last few days the UK death rate has risen alarmingly,
currently running at around 0.35 (35% additional deaths each day), considerably
higher than the US mortality growth rate which as would be expected appears to
be converging on the case growth rate. If this trend were to continue, the UK
would have experienced 1,000 Covid-19 deaths in 5 days time, 1 day earlier than
the US. It’s not clear why the UK death rate should be increasing so rapidly;
maybe because of the lag in time between case detections and deaths, maybe
because of the populations initially infected. The most concerning reason would
be that even at this early stage the NHS is being stretched beyond capacity by
Some of the most important information about the Coronavirus (Covid-19) epidemic is to be found not from medical knowledge or in the lab but from basic mathematics. The key to understanding this behaviour is in the mathematics of exponential growth. What does this mean? There are two ways in which regular increases of anything can occur – either by constant addition – arithmetic growth – or by constant multiplication – exponential growth. We can illustrate the difference by starting from 1. If there is daily arithmetic growth of 2, then on the second day the total will be 1 + 2, so 3, on the third day the total will be 1 + 2 + 2, so 5, on the fourth day 1 + 2 + 2 + 2, so 7, and so on. If there is daily exponential growth of 2, then on the second day the total will be 1 × 2, so 2, on the third day 1 × 2 × 2, so 4, on the fourth day 1 × 2 × 2 × 2, so 8, and so on. The difference is in the sign – a plus sign in the case of arithmetic growth, a multiplication sign in the case of exponential growth. As is made clear by Chart 1 below, although the arithmetic growth gives higher totals initially, exponential growth very quickly afterwards leads to higher and rapidly increasing values.
Epidemics cause exponentially increasing numbers of
cases because for every person who is infected, that person can in turn infect
another. The number of people each infected person in turn infects every day multiplies
the number of cases. If we start off with one person who then infects one
other over 24 hours, and these two each infect another over the following 24
hours, and all four infected each in turn infect one other the next day, and so
on, then we have the daily exponential growth of 2 we described above. This
might be quite an extreme epidemic, but in any case where the number of new
infections is increasing each day, the growth will be exponential, rather than