Category Archives: Coronavirus

Coronavirus Update 25/04/2020 – It’s Too Early to Lift Restrictions

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.

Chart 1: UK and US Covid-19 Confirmed Cases and Deaths to 23rd March 2020 on a log scale – Data from www.worldometers.info/coronavirus/

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.

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Coronavirus Update 09/04/2020 – Light at the End of the Tunnel?

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)

Chart 1 – Data Source https://www.worldometers.info/coronavirus/
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Coronavirus Update 26/03/2020

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.

Chart 1 – Data from https://www.worldometers.info/coronavirus/
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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.

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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.

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