Tag Archives: healthcare

Coronavirus Update 20/03/2020

Current Trends in the UK and the US

More or less as I was posting my previous piece, the UK government was publicly rolling back on the idea that the aim of ‘herd immunity’ was the optimal strategy in the face of the Coronavirus epidemic. At the same time it published the scenario modelling of the Imperial College COVID-19 Response Team, which contained the following passage.

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 the epidemic.

Chart 1 – Data from https://www.worldometers.info/
Continue reading Coronavirus Update 20/03/2020

The Mathematics of the Coronavirus

Epidemics and Exponential Growth

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.

Chart 1

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 arithmetic.

Continue reading The Mathematics of the Coronavirus

Explaining the NHS Crisis: Lies, Damn Lies and Health Spending



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

Some thoughts on drug policy

Former Home Office Minister under Labour, Bob Ainsworth MP, has ’embarrassed’ his party leadership by claiming that ‘prohibition isn’t helping [and] the ‘War on Drugs’ is failing’.

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

NHS Reform – for Worse or for Better?

Published on Left Foot Forward on October 5th

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?