As anticipated, the Coronavirus outbreak has definitively entered new phases in both the UK and the US, in the wake of ‘lockdown’ restrictions limiting non-essential production and consumption and encouraging populations to stay at home. These policies are centralised in the UK and State-wide in most of the US. As we can see from Chart 1 below, the log curve of cases and deaths is steadily flattening to the extent that we no longer have exponential growth of cases and deaths. It seems fairly clear that significant bending of the case curves took place after widespread social restrictions were imposed, and that the death curves followed with around a 10-day lag.
It’s too early to lift restrictions
It is utterly irresponsible to suggest, as many are doing (Trump supporters in the US and the usual Brexit suspects in the UK) that this means that we are in the clear and can now start to contemplate lifting restrictions on gathering socially, for work and on public transport. We do not have exponential growth, but despite all our efforts we still have steady linear growth in cases and deaths as indicated in Chart 2 below, and more clearly for deaths in Chart 3. Linear growth means that roughly constant numbers of people are acquiring the disease and are dying from it daily.
It is notable the extent to which the UK and US patterns of Covid-19 growth are now following each other, with similar rates of case growth and of the rise in deaths from the Coronavirus epidemic. (Chart 1)
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.
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
Just how much cash does the NHS and social care need to prevent the distressing stories of patients languishing on trolleys for hours in A&E departments? Can we possibly afford what it needs, or is it really a ‘bottomless pit’ as often claimed? Do we need to lower our expectations of what can be provided for us? Or does the whole funding system of the NHS need to be overhauled, with charges and/or insurance-style payments? Sadly, we are frequently being directed by politicians’ state-shrinking agendas and commentators’ ignorance towards the wrong numbers and the wrong reading of those numbers, with the result that the wrong answers are given to these questions. The truth is that if we look at things correctly, there is no reason why we cannot have an excellent healthcare system in Britain without any great sacrifice in our enjoyment of the other goods and services that the modern economy has to offer. Continue reading Explaining the NHS Crisis: Lies, Damn Lies and Health Spending→
I would think that one useful way of approaching the issue is to consider the balance of harms affecting drug users (who choose to use drugs) and non-drug users (who choose not to). Currently non-drug users suffer from the violence and crime associated with the illegality of drug use and supply and pay the costs of countering them, and they have to cover most of the costs of treatment for the results of poorly-prepared street drugs and of addiction. Continue reading Some thoughts on drug policy→
Under the coalition’s planned NHS reforms GPs could find themselves with a serious headache. Patients armed with detailed outcome data and on-line hospital reviews may enter a GP’s surgery demanding referral to a named specialist at a hospital in another part of the country. The patient-choice imperative will make this a difficult request for that doctor to resist, but the financial and commissioning responsibilities handed over by the reforms may give him or her a worrying conflict of priorities.
A traditional role of the GP in the NHS was as a ‘gatekeeper’, who filtered out those of his or her patients most likely to benefit from specialist care, and referred them according to knowledge of the local hospitals and consultants. In this way, costs were kept down, capacity constraints observed and quality was managed through professional reputation. Now that paternalism is a dirty word, self-diagnosis takes a few mouse clicks and professionals are no longer trusted by default, this is no longer acceptable. Continue reading NHS Reform – for Worse or for Better?→