Very simple modelling shows the case and death rate in an epidemic, such as of Covid-19, to be highly sensitive to both the timing of measures to prevent transmission, such as lockdowns, and the effectiveness of such measures. Lockdown later in its epidemic than in the Chinese case explains the higher incidence and mortality projected for the UK compared to that which occurred in the initial Chinese outbreak.
Lies, damned lies and statistics
Disbelief and denial are the order of the day.
There are claims in the US that: “The Chinese Communist Party has lied, is lying, and will continue to lie about coronavirus to protect the regime.” Now, as I’ve noted before, the fact that the death rate in Wuhan was reportedly several times that in the rest of China is most likely due to the fact that fewer of those infected were tested in Wuhan. The actual infection fatality rate (IFR) in Wuhan was most likely comparable to that in the rest of China, implying the infection rate in Wuhan was of the order of 3-4% of the population and, in the rest of China, much, much less than that, because of effective testing and contact-tracing. This observation is one thing, but it’s a very different matter to claim that China is lying about the extent of its epidemic and that (as is seemingly alleged) both case and death rates were much higher than reported. I suggest such a claim is fake news that there has been fake news.
More subtly, in the UK, Sir Robert Lechler, President of the Academy of Medical Sciences, claimed yesterday on Channel 4 news (from around 11 minutes in; video available only temporarily) that: “…at the moment we really are not sighted on what fraction of the population has been infected nor, by the way, is any other country as far as I know.” Well, as I understand, antibody tests are in use in China and elsewhere, so the veracity of the final part of Sir Robert’s claim is highly questionable. Furthermore, estimates of the IFR in the Chinese epidemic have been determined by a number of different methods to be 0.6-0.7%. A paper confirming earlier findings was published in the Lancet (pdf) a few days ago.
Lechler presumably hopes that, by (as we shall see) letting the epidemic run for a bit, a significant proportion of the UK population will have been infected, and therefore become immune, giving the whole population some “herd immunity”. This would be contrary to modelling by Edge Health and others which suggests only a few percent of the population are infected (but approaching 10% in London), and we would therefore need to allow many more phases of epidemic growth and lockdown for even 50% – the minimum for herd immunity – to have been exposed to the virus.
It is of course possible that there have been more asymptomatic cases than anyone has realised. But enough to radically change the situation? I very much doubt it. That’s wishful thinking. And surely, if that were the case, epidemiologists in other countries in Asia, as well as China, would have realised by now and informed the world.
No, the reason the UK, US and many other countries are experiencing worse Covid-19 epidemics than in China is that they left it longer before taking drastic action to reduce transmission of the virus.
A very simple epidemic conceptual model
I’ve created a very simple spreadsheet to model a notional epidemic. It is a purely conceptual model: it’s not meant to represent the behaviour of Covid-19 with any accuracy, but the numbers are of the same order of magnitude.
I start with one case on day 1 and consider two scenarios: in early intervention measures are taken from day 30; in late intervention from day 40.
There are 3 parameters for exponential growth rates;
– the unrestrained growth factor (GF) – the increase in case numbers day on day before intervention;
– the stabilisation phase growth factor (SF) – the day on day increase (or decrease) over the 10 days after intervention, to represent the period when transmission continues in households and amongst key workers who can’t be locked down;
– the control factor (CF) – the decrease (or increase) in cases per day after the initial 10 days (not 0 because transmission will continue to occur, in shops and amongst health and other workers who are not isolated in households, for example).
In Fig.1, GF is set to 1.3, so that, before intervention the number of cases each day is 30% greater than that on the previous day. 1.3 implies doubling in slightly under 3 days, roughly that observed for Covid-19. SF is set to to 1.1, representing a 10% daily increase in cases for 10 days after intervention and CF to 0.8, representing an imperfect lockdown.
I repeat, nothing is different between the “Early” scenario and the “Late” scenario except for a 10 day delay in intervention. Late intervention results in dramatically higher case and therefore death rates. Fig 2 shows cumulative case rates in the two scenarios:
Figures 3 and 4 show daily and cumulative case numbers, respectively in a more aggressive lockdown scenario where SF is set to 1 (rather than 1.1) and CF to 0.7 (rather than 0.8):
As can be seen, the cumulative number of cases is sensitive to the strictness of measures to prevent transmission. The total number of cases in the conceptual model is nearly 50% less in the aggressive scenario than in the base scenario (Fig 4). And the time it takes to reduce the number of cases to a very low level is also much less in the aggressive scenario (Fig 3). Since the model parameters were really only tweaked (SF reduced from 1.1 to 1 and CF from 0.8 to 0.7), there’s clearly scope for even more dramatic effects of more effective lockdown action.
I repeat, this is only a conceptual model, but we are dealing with very simple maths here and similar effects will be expected in the real world.
Comparing the UK with China
Wuhan was dramatically locked down on 23rd January. How early was this in the epidemic there?
One measure is the number of deaths that had occurred. On 23rd January there were a reported 8 deaths in Wuhan, with a cumulative total of 25.
When was the UK epidemic at a comparable stage?
According to the figures published daily by the UK government (which I’ve been recording), 10 patients were reported to have died in hospital after testing positive for Covid-19 by 13th March and 21 by 14th March. It’s emerged over the last few days that deaths are not necessarily being reported immediately, but let’s take 14th March to be a similar stage in the UK’s epidemic to 23rd January for Wuhan.
The UK only went into lockdown 10 days later, on Tuesday 24th March, after the Prime Minister’s address to the nation on 23rd. I know it seems like a month ago, but we’re still only in week 2!
The good news is that many had started working from home a week earlier (chez Joslin became an office on Monday 16th). The bad news is that (anecdotally) the UK lockdown is not as strict as that in Wuhan.
So let’s say the UK took decisive action to stop transmission 10 days later than the Chinese did in theirs. With case and therefore death numbers doubling every 3-4 days we can expect an epidemic 5-10 times larger than that in China, similarly to the difference between the “early” and “late” scenarios modelled above.
China has experienced around 3,000 deaths. And, as Stephen Powis, NHS England National Medical Director said a few days ago, the UK will do well to keep deaths below 20,000. At a 1% IFR that implies 2 million cases, around 3% of the UK population.
Perhaps we should have gone into lockdown a few days earlier.