Firstly, this article is my own view and not representative of SigmaPro as a whole. Secondly it is not intended in any way to trivialise the fact that so far, over 66,000 people have lost their lives as a result of Coronavirus across the World. To lose a loved one under any circumstances is a terrible thing, especially when one feels that it could have been prevented, and our thoughts and prayers go out to anyone that has been affected directly or indirectly by coronavirus.
According to the World Health Organisation (WHO) coronavirus disease (Covid19) is an infectious disease caused by a newly discovered coronavirus. The Covid19 virus spreads primarily through droplets of saliva or discharge from the nose when an infected person coughs or sneezes, and the droplets land on another person close by and may in turn infect them.
The first recognised death from Covid19 was in China was on 10^{th} January 2020, one month later the number dying per day being above 100. So far, over 1.2 million people around the World have been infected, and while more than 250,000 have recovered there remain over 900,000 active cases. But how long will this go on for and how many people will die in the UK? Professor Neil Ferguson, of Imperial College London, warned that up to 400,000 people could possibly die of Covid19 in the UK. This is based on 60% of the population being affected, and a roughly 1% death rate.
(68,000,000 x 0.60 x 0.01 = 408,000)
But is that likely? Professor Ferguson is clear that he is not forecasting these numbers, but it is a possible worst case scenario. So, if not 400,000 what’s the most likely outcome?
This is a question I have been asked quite a few times, and I’m sure many others have also been asked the same question. So, how does a qualified engineer, not an epidemiologist, but a certified Master Black Belt with some basic understanding of statistics approach this kind of question, and what’s the answer?
Well the answer is 16,600, and the deaths from coronavirus in UK could continue to seriously affect us for another 4045 days until the 18^{th} May 2020.
But, how do we get to 16,600 and what are the assumptions involved, assumptions being a key part of the answer, because we don’t know everything we need to calculate the answer accurately, and of course the statistics involved are a simplification of what’s actually happening. But, for those involved in running improvement projects, think of this as the Define phase, we often use data which we are not sure of, and calculate estimates using it. In the Measure phase we move on to making sure we get the data we need and that it is accurate data.
The first answer I gave some weeks ago when first asked the question after there had been only a handful of deaths in Europe, was to look at the situation in China, which was then being brought under control, use their death and infection rate proportions and apply them to the UK population.
The problem with this approach is that it assumes the same infection and death rate and also assumes that the statistics quoted from China apply to the whole country, which is not actually correct. In fact the outbreak was mostly restricted to Hubei province, which has a population of 57 million, a similar size to Italy or indeed the UK. If we do the same calculation again but using 57 M, then we get:
Hubei: 57 M people, 3,300 deaths = 58 deaths/million of population
UK: 68M people x 58 = 3,944 likely deaths
However, the lockdown restrictions in China (Hubei) were stricter than those we have seen in Europe, in Wuhan for example all public transport, including buses, railways, flights, and ferry services were suspended. The Wuhan Airport, railway station, and the Metro were all closed. The residents of Wuhan were also not allowed to leave the city without permission from the authorities.
These restrictions, introduced on the 23^{rd} January 2020, did seem to have an effect, but the deaths continued to rise for some weeks afterwards, with the daily rate starting to reduce in mid February. It took until mid March for the numbers dying each day to be consistently in single digit numbers.
Figure 1  source www.worldometers.info
In Europe, Italy was the first country to have an outbreak of Coronavirus, with the first recognised death being recorded on February 21^{st}. The spread of the virus in Italy was far more rapid than had been seen in Hubei, by 10^{th} March the number of people dying per day was into the 100’s and after 30 days had reached almost 800 deaths per day.
Figure 2  30 days deaths in Italy
The lockdown restrictions in Italy were not as stringent as in Hubei, and were introduced more slowly, starting with restrictions on the 24th February in certain areas with lockdown across the whole country on the 9^{th} March. However, even then public transport was allowed to continue.
So, we can assume the spread of the virus is different in Europe (Italy in particular) to that seen in Hubei. Using data from the first 30 days, we are able to fit an equation that describes the pattern of deaths in Italy.
Regression Equation
Italy = 67.4  21.54 Day + 1.356 Day*Day
We can use this equation to predict the number of deaths going forward in Italy beyond 30 days and compare them with actuals. This allows us to see whether the lockdown measures in Italy had any effect.
It would certainly appear that the predicted deaths do not match what actually happened in Italy, supporting the fact that the measures did have, and are having, an effect. The actual curve no longer looks like an exponential increase. Note that it appears to be actually reducing from a peak of around 900 deaths per day. If we use a Poisson regression analysis to find this new equation, the best fit now looks like this:
Regression Equation
Italy 
= 
exp(Y') 


Y' 
= 
0.927 + 0.4127 Day  0.005686 Day*Day + 0.000003 Day*Day*Day 
Again, we can use this to estimate the number of deaths in the coming days, and if we add these predictions to the chart we get the picture below:
The graph shows a typical scenario. Worst case (95% confidence) shows that by day 75, deaths should be in single figures in Italy. Day 75 is the 5^{th} May. The total number of people dying from Covid19 in Italy during the period is the area under the curve, which is around 20,000 deaths. 95% confidence upper limit shows around 21,500 deaths.
But what about the UK? Although the number of deaths per day in the early period in the UK was similar to China and not Italy, the implementation of the lockdown measures in Italy, rather than China, seem more similar to the way measures have been implemented in the UK in both timing and detail, and in the last 2 weeks the number dying has risen more steeply than seen in China. Therefore, one could argue that Italy makes a better model to use if we want to estimate how the lockdown might affect number of deaths in the UK.
Assuming that the populations are the same, we could use the first 30 days of deaths in the UK, and then the prediction equation data for Italy for the days from 31 to 75 with an adjustment for the slightly lower values generally seen in each day in the UK (on average 86 less), then find the equation that best describes this data. This equation is:
Regression Equation
UK 
= 
exp(Y') 


Y' 
= 
4.195 + 0.6245 Day  0.01004 Day*Day + 0.000029 Day*Day*Day 
If we use this equation to draw the prediction graph for the UK it looks like this:
If we add the area under the curve going forward from today to the existing deaths that gives a total number of deaths of 16,617, around 17,500 if we take a 95% confidence worst case scenario. It is likely that the deaths will continue to affect us for another 4045 days, going through to the 18^{th} May.
As stated at the beginning of this article, there are a number of assumptions involved, because we don’t know everything we need to calculate the answer accurately and the statistics involved are a simplification of what’s actually happening. It also assumes the underlying data is accurate, which of course is not guaranteed. It also, of course, assumes that the lockdowns continue and people stick to the restrictions introduced to safeguard lives and protect the health services.
There also many other questions that are not covered in this article, not least the differences in regions, the concept of “herd immunity”, the role of testing and PPE, the economic impact, and what happens when restrictions are lifted.
And finally, just to emphasise that our thoughts are with anyone who has been or will be affected by Covid19, their sadness and loss cannot be measured in statistical terms.
Chris D. Rees
Director of Operations, SigmaPro Limited
06^{th} April 2020
References
https://www.worldometers.info/
https://www.who.int/healthtopics/coronavirus
https://www.standard.co.uk/news/health/coronavirusbritainukdeathsa4362866.html
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