15 April 2020

COVID-19 Epidemiology, Part 5

COVID-19 Epidemiology, Part 5

(All my data are from the government site: Coronavirus (COVID-19) cases in the UK ; Last updated 14 Apr 2020, 3:44 pm GMT.)

     The news for the United Kingdom of GB continues to be mildly good. The 'doubling-time', measured in days, which is my chosen index of the spread of the virus through the population, was steady at 3.5 - 4 for the 13 days prior to the 24th March (see Fig. 1). 
     On the 24th March the government instigated what we call 'Lockdown' which closed schools, and many shops, cancelled many trains and busses, instituted restricted numbers inside food-shops, and many other curtailments. 
     It took some time for the public to get behind these restriction, but they are now very widely observed. Since the 24th of March the doubling-time of the total case-count has started to climb, and now climbs persistently. (See Fig. 1) On 14th April the doubling time was 12 days. 

Fig. 1  depicts the un-smoothed data as the increment in the total case-count, converted to 'doubling-time' in days. The horizontal axis is 'days' before and after 31st March

     Another very good measure of success in curbing the spread of this (or any other virus), discussed by Professor Trisha Greenhalgh and Jeremy Howard (1), is the transmission rate, i.e. the number of new infections generated by an infected person. If that number is greater than 1.0 the virus spreads; if less than 1.0 the epidemic dies out. COVID-19  started out with a transmission rate of 2.4. The paper by Greenhalgh and Howard (1) goes on to show how masks reduced the COVID-19 transmission rate in several countries. 


Reference:

09 April 2020

COVID-19 Epidemiology, Part 4

COVID-19 Epidemiology, Part 4

     The good news this morning, for the UK, is that the country seems at last to be learning how not to catch the new Corona-virus. The doubling-time (in days) for 'total reported cases' has climbed steadily from the 2nd of April and is now (midnight 8th April) at 9 days. (See graph)
     The bad news (for those living in the rural county of Northamptonshire) is that Northamptonshire seems to have learnt nothing to date; no doubt living in the fool's paradise of thinking that "there are no case here". Well, there are cases in Northants.; and they are doubling in number every 41/2 days. 


Graph: Doubling-time against date in April 2020
For doubling times and other terms and calculations see previous entries in this blog.

COVID-19 Epidemiology, Part 1
COVID-19 Epidemiology, Part 2
COVID-19 Epidemiology, Part 3


05 April 2020

COVID-19 Epidemiology, Part 3

COVID-19 Epidemiology, Part 3

I continue to plot the Log of UK cases (and deaths) each day (See COVID-19 Epidemiology, Part 1 and COVID-19 Epidemiology, Part 2.) However, the 'cases' data no longer fit a logarithmic plot; the growth is slowing. If I take the daily increase in the logged data for the period 16th - 24th March and plot that against the date (day 0 is 4th March), the data are (of course) rather wild. But the average daily rise is around 0.086 corresponding to a doubling-time of 3.5 days (0.3010/0.086 =3.5). Steady!

On 24th March lockdown in the UK was instituted in earnest. There is a very noticable change in the slope of this plot of 'Daily increment of log cases' against date. Over the 11 days 24th March - 4th April the calculated doubling-time has gradually (albeit erratically) risen and is now around 7 days. That is good news. 




No similar improvement is yet visible in the log(deaths)/day curve; doubling-time remains around 3.24 days. Presumably that is because there is a time-lapse of around a week between showing symptoms and dying. We must hope to see an improvement in the next few days regarding the data on deaths from this troublesome virus.

I understand that the 'cases' data from Mexico show an increase of around 10.5%  per day. That is to say, it is still logarithmic, with a doubling-time of close to 7 days. (0.301/Log(1.105)=6.942)

30 March 2020

COVID-19 Epidemiology, Part 2

COVID-19 Epidemiology, Part 2

I continue to track the UK data each day, recording now the reported 'deaths' as well as 'cases' ❋❋. And I continue to plot the Log(10) and find a straight-line; i.e. there is a good fit to 'logarithmic growth'.  But, in order to make my curves responsive to good news in the form of a slowing in the rate of transmission, I plot only data from the last 7 days. Currently (data to 29/3/2020) I find a doubling time of 3.8 days for cases, but 3.3 days for deaths. 




John Burn-Murdoch (@jburnmurdoch) Tweets on Sunday 29th that the doubling time for the death toll in 2.8 days. I wonder why the discrepancy. (And would appreciate discussing this in detail: cawstein@gmail.com)

(❋❋ I realize that there is some doubt as to 'cause of death' when COVID-19 is present, and some doubt about 'cases' when tests are not used, but those problems are inherent in the data, and not my problem here.)

22 March 2020

COVID-19 Epidemiology, Part 1

COVID-19 Epidemiology, Part 1

    I have been tracking the numbers of reported cases in the UK each day since the 4th of March, and plotting the logarithms on a spread sheet. On my semi-log plot, the slope of 'line of best fit' on 21st March was 0.1035 which corresponds to a doubling time of 2.908 days.  Assuming that the doubling time remains 2.908 days, the extrapolation to 14th April (41 days from the 4th March) indicates 1,573,620 cases of COVID-19.  


    There are odd points that lie off the line, probably showing how difficult it is to get data pertaining to a standard time of day. There may be a slight amelioration in the rate of infection during the last week, for when I calculated the 'line of best fit' on day 12 the doubling time was 2.77 days, extrapolating to 1,906,777 cases by 14th April
[Keep an eye on this space for I shall add updates,
 as the data accumulate.]
    The naif average death rate in UK on 20th March was 177 deaths per 3,983 cases cases, i.e. 4.44%. That is likely to be an underestimate as some 'cases' may become 'deaths'; but, if that ratio of deaths to cases is maintained for the extrapolated 4 weeks, we would have, on 14th April, a UK death toll of 69,869.
     To put that in context, there were 1,793 road deaths in the UK in 2017. We have not experienced a pandemic of this scope and gravity since the 'flu epidemic of 1918/9 which claimed 228,000 lives in the UK (when the population was 43.9 million).
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    The UK Government is now trying to lower the current rate of spread. From 23rd March, schools and universities are to be closed, and train services are to be curtailed. There is a clamp down on social mixing in pubs and restaurants. The measures are stern but not 'draconian'. We shall look for a change of slope on the semi-log plot, but only after the incubation lag of perhaps 7 days.
     The doubling time is presumably determined by the number of transmissions per case. Modelling of this process is useless without accurate data; the number of unknowns is considerable. Suppose that an uninfected person (A) internalises a virion on day 0, which multiplies internally for 6 days when the host starts to shed virions, i.e. becomes infectious. Suppose symptoms appear on day 7 and continue till day 14, while shedding of virions continues till day 21.  The most dangerous period is clearly between days 6 and 7 for 'cases' will probably become more careful when they know they are infected.
    But this is idle guesswork. We need data.


                       






22 February 2020

The Romance of Re-wilding

The Romance of Re-wilding
  Isabella Tree is to be congratulated for her recent book “Wilding: the return of nature to a British farm”. (Picador, London, 2018, ISBN 978-1-5098-0510-5).   It is a thrilling evocation of what I am calling ‘the romance of re-wilding’.  Her book is well written, well illustrated and well researched. We learn, as we read, a load of botany, zoology, and soil chemistry expounded with clarity and confidence. We meet amazing, charismatic and admirable people. We accept their values, share their excitement and recognise their triumphs.
Of course we are delighted at the return of turtle doves to the Burrells’ farm; who would not be? And their stunning success with the purple emperor butterfly. Part of the thrill of seeing a kingfisher has, in my lifetime, been its rarity, but only part for much of the thrill is in the startling brilliancy of its plumage, and the darting swiftness of its flight; kingfishers would thrill anyone, even if they were seen every day, just as hummingbirds never fail to astonish. 
The magic of re-wilding seems to lie partly in its spontaneity. We stand back and watch a natural process; almost as though there were a single conscious purpose at work on a preordained plan; we seem to witness ‘Mother Nature’. The willows come back to exploit the soggy soil, the butterflies to exploit the willows. No doubt the swallows and flycatchers will enjoy the insects, and the peregrines will enjoy the swallows. It all fits. It feels right. 
I am tempted to muse on in the same quasi-religious vein. Just as ‘Gross Domestic Product’ is a summation of all the incomes of all the people in a polity, so it seems there should be a quantity we could call ‘Satisfaction’, that is the sum of all individual satisfactions in a polity. It is not immediately obvious, but my hunch is that ‘Gross Domestic Satisfaction’ is maximised when there are least constraints, when each player moves from a position of less satisfaction to one of greater.  Be that as it may, there seems a bonus when watching nature take its course, in feeling that every player is doing what it wants, be it a fungus, or a roe deer.
It is common, and understandable, to bemoan declining numbers of curlews, song thrushes, and cuckoos in the British countryside, because they make such thrilling sounds; they speak ‘springtime’, ‘sun’, ‘sex’, and ‘summer’. We naturally feel that we are being deprived (by someone) of our rightful inheritance when we find them gradually vanishing from our lives. Furthermore, it is easy to feel the same indignation about the threatened extinction of crested newts, crested cow-wheat, and lady’s slipper orchids; even when we have never seen them and never looked. 
To experience, and may I even say to indulge, these emotions is what I am calling the romance of re-wilding. The word ‘romance’ justifiably indicates the high emotional content, the free play of imagination, nostalgia, and hope. There is a swelling of the heart at the very thought of Nature returning. 
We know, of course, why our ancestors dredged and drained, uprooted hedges, enlarged fields, mechanised, sprayed, and specialised. It was to raise agricultural output. It seems that the population of Britain never much exceeded 6 million between the Roman period and 1700. There were peaks in 300 A.D., 1300, and 1650, but troughs between, with the ‘dark ages’, the ‘black death’, and the ‘mini-ice-age’. The limit seems to have been set very largely by food production. After 1750 the UK population rose from 7.8 million, to 10.8 in 1800, to 27.1 in 1851, to 38.2 in 1901, 50.4 in 1950 and to 67.7 million today (i.e. in 2020).  As food production rose, so did population. From 1850 food imports became important. Currently we import some 40% of our food.  
Of course, there is a lot of land in Britain that is not dedicated to food production; we could re-wild that. Waste land, old railway sidings, drove road verges; that would be wonderful. One of my enthusiasms is ‘wild-life corridors’ linking city parks and town moors with the surrounding countryside. One or two farms could re-wild if they were better able to produce butterflies than profits. But it does not seem realistic deliberately to lower food production without a concerted programme to lower the human population in parallel. 
Our emotions are hard to reconcile with good sense. I do love an expanse of  fresh, young, heather, but I know that it takes a lot of husbandry to keep it like that,  grazing and burning.  I once saw the dramatic effect of a deer-fence in an area near Torridon that was once part of the ‘Caledonian Forest’. The shallow slopes were soggy, hag-ridden, peat topped by leggy heather, sundew, and sphagnum. A small area, between the size of a tennis court and a foot-ball pitch had been fenced round with a high fence. Spontaneously the pines had appeared and were now anything from 1 to 10 metres high. Deer or pine; each has its emotional appeal; but without wolves we cannot have both. 

Re-wilding our country is a wonderful thing to look forward to, and we can hope for more and more of it as we work our human population down towards the 6.5 million we had in 1700 when wolves vanished from our island.

08 January 2020

Open letter to Greta Thunberg

Dear Greta Thunberg,
    I wonder if you will ever get this letter. I feel like someone stuffing a message into a bottle, corking it up tightly, and dropping it overboard. 
    I think you are doing an amazing, valiant, and most creditable job, in drawing the world’s attention to the global climate crisis. To an intelligent person it clearly seems nigh unbelievable that so little is happening to cut carbon emissions so long after it became clear that the global temperature was indeed rising. But I want to make two points. 
    Do not burn yourself out too young; keep something for the ‘long-haul’. The world has had the message for a decade now, and that message is getting heeded in a few areas of hyper-intelligence (e.g. Scandinavia?).  Perhaps another decade and we shall start to see the beginning of a massive change in habits, and countries vying with each other to be front-runners, instead of watching each other so as not to be first to flinch. 
    And do not let us exaggerate the crisis. It is not as though the world were spirally rapidly into the sun with disaster expected on a 20 year timescale. I am a committed believer in the man-made  origin of the global temperature-rise, and believe the finger points largely at our carbon dioxide blanket as the main cause. I am very impressed at the scientists's prediction of this ‘green-house’ effect so many years ago, and at the great mountain of data that now exists to substantiate it. But I understand that this has happened many times before. The laying down of layer after layer of coal suggests that periods of high atmospheric carbon dioxide lead to massive deposition of plant remains. Another great store of carbon dioxide exists in chalk and limestones deposits, going back hundreds of millions of years. Of course the sea level and global temperature has risen and fallen massively over that time scale. And it is no recompense to the burned and drowned to know that probably, on the basis of current evidence, the world and its more successful species will survive. Still, it is some consolation. 
    Look after yourself. We shall need your intelligence, and clarity, in ten years time just as much as we do now. If each of your converts themselves converted 2 others, we would get the message across in time. For me, the way out seems to be increased use of solar energy, decreased use of fossil fuels, planting trees, and reducing the human population intentionally and voluntarily. (So much better than the reduction in human population unintentionally and involuntarily.) 
    If you get this and would like to comment, please send a message to me at cawstein@gmail.com. I would be glad to hear, be it only of my errors.