Tag Archives: exponential growth

COVID-19. Simple Arithmetic and ‘The Economy First Delusion’. PART 2.


I’d like to think that the most democratic countries have been the best at controlling COVID-19, but this would not be true, although there is no doubt that China did a great job at under reporting the severity of its outbreak, claiming that any suggestion that this was a  problem originating out of China as racist. There was little about the way China reported on its outbreak that would help other countries to prepare.

In the U.K. by 8th April over 60,000 had tested positive for COVID-19, with more than 7,000 deaths as a result of the virus. At the peak of the problem the British Prime Minister Boris Johnson was taken into intensive care, and the good news is that he is showing signs of improvement. It is a little over a couple of months since the first confirmed case in Britain and today alone there have been 938 hospital deaths with 5,492 new cases announced; although there is a claim that infection numbers have increased because more people are now being tested… and a fair response to that would be: testing? Not before time.

This is a very different world from the one where we were wishing our friends a happy 2020 back in January. For many of us, staying at home has so far been voluntary, but last weekend it was sunny and springlike in many parts of the Northern Hemisphere and against official advice quite a numbers of people were out and about with a minority of Brits refusing to conform to anything that felt like an intrusion of personal freedoms. They knew  that if they went out for a wander, nobody was going to shoot them – which is a pity: and I’ll leave that sentence as it is… ambiguous. Unfortunately, some things don’t change – there will always be people who don’t have the discipline to act appropriately, and potentially set back the slowing of COVID-19 infections.

France, has a similar problem: on the 7th of April the lockdown became more severe – the first case in France occurred a little over 10 weeks ago, but by the 7th April the death toll had passed 10,000. That was the figure for Italy almost a week ago and there are claims that the French figures have been distorted, with numbers far higher than official figures. France is now one of the hardest hit European countries. Spain’s death toll has passed 14,000, although both Italy and Spain appear to be at the point where infections are beginning to slow.

But how did South Korea, one of the earliest countries to be hit by the virus, manage the disease so much better than many of the Europe countries, limiting the disease so far, to less than 10,500 infections and 200 deaths. This might well have been aided by experiencing an outbreak of the MERS virus in 2018, but more likely it is down to the way things are organised in South Korea. The country has a very good healthcare infrastructure which isa  plus; and there is a centralised control of decision making and that has been key to getting things done. The country tracked infected citizens in an authorised manner by monitoring locations for cell phones and credit cards. We are told in the west that such a thing would be impossible, unless of course somebody is trying to sell us something, but when done for public health reasons it is an infringement of personal liberties.

Obviously, the South Korean approach would not work everywhere, and in the long term the disease will re-emerge because so few people have so far been infected – you can’t have it all ways; but if anything is to be learnt from this method, it is that a TEST, TRACE and QUARANTINE policy really does work, although many other countries have failed to do this effectively. The best part of the story is that when things started to go badly wrong, South Korea put scientists in charge, and once clear on what needed to be done they acted swiftly, without any kick back from members of the public advocating all the various alternatives to science based decision making. Alternatives to common sense might be absorbed under normal circumstance, but when thousands of people’s lives depend upon governments making reliable decisions on a daily basis, there’s no time for nonsense; and any fool that refuses to make minor short term lifestyle changes to allow others to stay alive, demonstrates about as much discriminatory ability as the virus that the authorities are trying to contain.

COVID-19 is one of the most difficult global problems we have faced in recent time, but this is no longer because people are carrying the disease by flying to new destinations the way they were just a few weeks ago. Now that most commercial flights have been grounded, air quality has improved enormously and there has been a reduction in Carbon emissions. Ironically, as the virus attacks airways in human bodies, airways in the skies have also been depleted, resulting in cleaner air, which makes breathing a healthier experience for all of those who have so far managed to avoid the infection.

In many places in the world, you might think that things can’t get worse, but not if you live in the U.S.A.. It is difficult to find a better example of what dithering can achieve when dealing with a rapidly spreading viral infection; a problem largely ignored during the early stages of the outbreak. In the U.S. there are necessary checks and balances to ensure democracy, but when decisions have to be made at both Federal and State level, results often lack a co-ordinated approach, and during a rapidly moving emergency as is the case with COVID-19, things don’t always go smoothly. Lacking almost any form of control, the virus sensed its freedom and quickly took off. It didn’t have a green card, but moving so fast, easily avoided apprehension. The virus just wasn’t tested and in consequence the U.S. is on the same trajectory for the infection as Italy was a few weeks ago, and will certainly pass it, which to say the least is unfortunate.

The U.S. has experienced a broad range of criticism over its dealings with the pandemic. Florida disease expert Dr. Dena Grayson made the point that the first case of Covid-19 in South Korea occurred on exactly the same day as the first case in the U.S. Jan 20th 2020. While South Korea had its first tests for the disease approved in a week, the U.S. spent most of February wasting time. Countries that have got onto testing early and in high numbers, have been winning the battle because they have a handle on what they are dealing with: knowing who is infected, the rate of infection, and where it is occurring allows the disease to be targeted. Acting without testing is like stumbling around in the dark; worse than that, it is like stumbling around in the dark in the Dark Ages… Getting testing up and running in the U.S. has been slow, and contributed to the spread and general lack of control of the virus in many parts of the country. But more recently President Trump started talking less about the economy and getting people back to work, and more about dealing with the virus, when previously he had down played the problems – hopefully this won’t have come too late to make a difference.

Certainly things are fairly dire with 10,000 deaths by 6th April. On 8th April 8th the daily figure for deaths in New York state alone hit 799, with almost 2,000 Americans across the country dying on a single day…  The same day President Trump swung back to his old approach as he made further comments about opening up the country for business, His advisers said that it was far too soon to loosen up restrictions, and are waiting to see what the President will say next; and it probably isn’t unfair to say that his message on the COVID-19 crisis has become increasingly erratic.

The U.K. like many other places around the world has gone for the personal distancing and isolation for those who are vulnerable or display symptoms, but early on, there was a more relaxed approach. The suggestion was that if enough people were to become infected, ‘herd immunity’ would slow the rate of infection and with less people available to infect, and the infection would drop away; but it soon became clear that with more people getting ill, the health service was likely to become overwhelmed. Britain already had the example if Italy, which was well ahead of other European contries with its stage of infection; and at home intensive care really did mean intensive and often prolonged care, which would become unsustainable as the number of cases increased. It was apparent that some countries had too few respirators and difficult decisions were being made on who lived, and who died. This didn’t go unnoticed by British politicians and there was a sudden change of policy. Maybe there really was an awareness that once an infection rate starts to climb the steep end of an exponential growth curve, ‘things fall apart’ but the decision making might have been more complicated than that, although if they just followed the science it probably didn’t need to be. 

The virus was a little slower getting to some parts of the world; and this was the case for Nigeria, where preparations were being made long before it arrived; especially in Lagos, which has around 20 million inhabitants, and is the most populated city in Africa.

In the capital city, one in three households live in poverty which makes dealing with any contagious disease difficult. This is true for any country that has large numbers of people living in close proximity to one another with poor sanitation, problems with clean water, and otherwise difficult conditions. In such places COVID-19 could prove devastating as local infrastructures prove inadequate when dealing with such a virulent disease. There is also a high probability that such locations could become reservoirs for COVID-19, with outbreaks continuing for years into the future.

We learn from every viral infection that has gone before. In 2009, a new flu virus emerged and was given the name (H1N1)pdm09, it would became a pandemic. This flu variation showed up in a form quite different from the H1N1 virus that had been circulating previously, but despite the differences older people appeared to have some immunity to it, perhaps because of previous exposure to the H1N1 virus earlier in their lives, and the disease would primarily infect younger people who had not had the same exposure to the H1N1 virus. Retrospectively, we can see trends with most viral diseases, but when a new one crops up, or returns in a slightly different form, it can be difficult to predict outcomes. One of the options is to closely watch a disease in its early stages, and extrapolate the numbers that the course of infection throws up and act accordingly.

Flattening the Curve.

With infections of COVID-19 doubling every three days both in the U.K. and elsewhere it became clear that if the virus was allowed to run its course without resistance it would overwhelm health services and make dealing with the virus impossible. The solution was to flatten the curve. i.e. to spread the number of infections over a longer period of time to avoid losing control. The policy required people to wash their hands, keep a distance from one other, and for the most vulnerable and the infected to self-isolate for several weeks, thus starving off opportunities for the infection to reach a new hosts. In Figure 1 an individual works away to flatten the curve. Above the red line, high numbers of infections will overwhelm the health service in a short period of time and put hard pressed health workers at greater risk of infection.

If the number of infections can be spread, keeping the curve below the red line as in Figure 2, the load will be reduced and make dealing with  the disease more manageable.

 On 20/3/20 bars and restaurants were closed in Britain encouraging people to keep their distance from one another – stay at home was the message. But around the world not everybody was listening to government advice. On the other side of the world large numbers of people were out and about in close proximity, enjoying themselves on Bondi beach. Perhaps embarrassed by the publicity, the New South Wales authoritie -, within a few hours of the story emerging – closed beach access. Then came the news that the day after tighter restrictions  in the U.K., people had responded by going out in Bank Holiday numbers to beaches all around Britain, with Brighton, Bridlington and Skegness especially busy. People were also travelling from heavily populated areas to remote locations such as the Highlands of Scotland in an attempt to escape the virus, potentially bringing the disease with them. Initially the message wasn’t getting through – clearly some people  weren’t taking the crisis seriously and valuable days were lost while government went about trying to provide a clearer message on why in the short term a lifestyle change was necessary.  By the beginning of April a sunny weekend became irresistible for some, and ‘the rules’ might need to be more rigorously enforced in future, especially at Easter, when the continued efforts of the majority could so easily be compromised.

The way beaches around the World should look where COVID-19 is a problem and people are obeying the rules. On the positive side, wildlife has more opportunities with fewer people on the move.

Maybe there’s a simple way to explain why we all have to modify our behaviours to combat COVID-19, because when simple arithmetic begins to look like maths, nobody wants to know, although in the U.S. it’s math, which makes it even more singularly dull. So, consider a hypothetical viral disease similar to  COVID-19: the number of people infected by the disease doubles every three and a half days and it is most infective during the first week after entering a new host, where it gets busy shedding rapidly to optimise the chances of entering other hosts. Under these circumstances a person infected by the disease will infect two other people over the course of a week, and those two people will each infect two others during the second week, and so on as the disease progresses. 

For no better reason than vulnerable people in Britain have been advised to isolate themselves for three months, let’s run the course of the disease over the same period and assume a vulnerable person comes out of isolation on week 13. If I was superstitious I’d describe this as the unlucky week, especially if the vulnerable person was to meet up with a ‘couldn’t care less infected individual running in a direct line of transmission from the original source.

Here’s how it goes: Harry is a bit of a twit and doesn’t like following rules; against government advice he’ll take his chances of getting infected. Harry is out and about and he doesn’t care: on the beach one day, in the park another, and drinking with friends in social gatherings. He has the virus in his system but shows no symptoms – the surprise is he infects only two people during his first week of carrying the disease and that’s how things start.

Over the course of twelve weeks Harry’s indifferent behaviour sets off a a progression of infections for which he is the only source; the infection of other individuals progresses week by week starting from the initial 2 infections in the first week, which creates 4 infections the second week, and so on. 4 becomes 8, 8 becomes 16 then 32, 64, 128, 256, 512, 1024, 2048, 4096, and by the unlucky 13th week, Harry has been responsible for 8,192 infections. Fortunately, the death rate is only at 1% of those infected – I have been generous because The World Heath Organisation gives a figure of 3.4% for COVID-19, but I’m thinking it might not be that high because there must be a lot of people infected who are not aware, due to a general lack of testing in so many places; and there must be a good numbers of people walking around who never get to a hospital. So, with the theoretical disease Harry has killed only 80 people and that’s well above what most serial killers will manage. Infact you’d probably have to go to war to kill that many people and get away with it. If it was as high as 3.4% Harry would be responsible for the deaths of 272 people

What if you were as irresponsible as Harry but you infected 3 people in a week rather than two, and things went on at that rate, tripling up rather than doubling up – a transmission rate that by some estimates would be low for Covid-19. The series would run: 3, 6, 12, 24, 48, 96, 288, 864, 2,592, 7776, 23,328, 69,984, 209,952 and if things went on another week, that would push the figure up to nearly half a million. With a death rate of  1% over just the 13 weeks there would be over 2000 people dead. What if  4 people were infected each week?… Perhaps it does make sense to avoid other people for a while… 

I will admit to a hole in this model. There will be people not going out in an effort to avoid Harry and other people like him, and so the more people who are behaving responsibly the less contacts Harry will make, but nevertheless amongst Harry’s friends, it isn’t too difficult to infect 2 people over the course of a week. Nevertheless, people distancing themselves from others will starve the disease and the number of people catching the virus will drop significantly. This is the reason models come in for so much criticism, they appear to be all over the place, with the predictive number of infections varying from a few thousand to hundreds of thousands, this not because the model is wrong, but because figures can change dramatically when small changes are made early in the progression of the disease. If we don’t get our behaviours right, the number of infections possible are sobering and demonstrates that simply doing the right thing can make a huge difference; and my figures might be regarded as low – to keep things simple I’ve only considered the number of new infections at the end of the 13 week period and not added in all the previous infections as the process moved along ( i.e. the overall total infection number). The same is also the case for the number of deaths.

There are only dummies in shopping malls now.

We could get bogged down with many other aspects of the disease, but for our purposes, all we essentially need to know is the rate of infection, which to some degree depends on how infective the virus is and how we might reduce its spread by our good behaviours. It would obviously be useful to know exactly who is infected and what percentage of the infected are dying, but beyond knowing how many people are behaving irresponsibly, most of the figures are out there, and it’s up to our governments to assess them and implement effective policies to reduce the number of infections and deaths as effectively as possible. We essentially are just the fuel in the equation – numbers on the graph – and need to stay off of the page if we possibly can.

A Canada Day past: it comes around on 1st July, but this year maybe it won’t look like this.

Test, test, test has been the mantra of the World Heath Organisation, and some  governments have been hopelessly ineffective at doing so (Ontario has the highest number of cases of COVID-19 and the lowest testing rates of all the Provinces in Canada…. Is that a coincidence?). In so many countries, as individuals, we need to stay out of circulation for a while – it’s the very least we can do for medical staff who’s lives we put at risk when failing to do so. Staying indoors for most of the day is inconvenient, but it’s better than being dead or causing the death of others.

Saving the Economy Versus Slowing the Disease – Let’s Look at It Another Way.

There’s a pilot with a dilemma. He has taken a small party of people to do business in a remote area of jungle and has to fly them home in a light aircraft. The plane takes off with everybody on board, but pretty soon the aircraft’s engine begins to misfire and the pilot wonders if he should perhaps land on one of the occasional small airstrips still available below and fix the engine; but he knows the businessmen need to get back, and so he flies on. Suddenly the engine begins to misfire very badly and the pilot reconsiders what he should do because the airfields are beginning to thin out now; but he thinks first and foremost of the businessmen knowing he must get them back to their busy lives of doing business and he flies on. But, he hasn’t flown much further when he begins to notice that there are now fewer airfields below just as the engine suddenly catches fire and begins to fail. By great good fortune the pilot sees one last airfield up ahead… he knows exactly what he must do…… he flies on.

For those entrusted with saving the economy it should be apparent that when dealing with an exponentially growing threat, the best policy is to fight that threat as early as possible, never underestimating the power that could be unleashed if you don’t, because when that happens, the price can be very high.

And maybe it’s worth remembering that money isn’t real, it’s value depends on whatever we convince ourselves it’s worth, whereas death isn’t negotiable. It might be that we have to adjust our economies to line up with the natural circumstances we are all living through, instead of allowing the majority to suffer when the loan sharks decide that it’s payback time. Once through the pandemic  we might be forced to live in ways that are less damaging to the environment, even though history demonstrates that major disasters do not in the long term halt our Carbon emissions; and there is no guarantee that the future will demonstrate that we have learnt anything useful from the problems we are now facing.

I appreciate the hardship caused to people who have been prohibited from working, but in part this situation is the fault of the many governments that have let things ride, hoping they could get away with it. They pushed their luck and they failed.

In fairness, COVID-19 is new to us and nobody can be absolutely sure at which point we might have done better as we were passed through it; but the figures should have provided at least an inkling, and at times it seems as if many minds have been busy elsewhere.

We haven’t been dealing with some abstract existentialist threat: just like the world’s airlines, this has been a grounded event  – an exponentially growing  disaster with nothing hidden from view. If only more politicians had recognised the danger signs earlier than they have, because many of the answers were sitting there quietly in the arithmetic – just waiting to be discovered.

COVID-19. Simple Arithmetic and the ‘Economy First’ Delusion.

Although most of us now have some idea of how to behave in the face of the COVID-19 pandemic, few of us understand how ‘the thing’ really operates, but we can still glean information from the freely available daily figures. Unfortunately, there are also a lot of politicians who don’t understand the virus very well either, despite having access to expert advice and a lot more information. One wonders if perhaps they had spoken more regularly to immunologist rather than economist, whether things would be different now, standing as we are on the  pandemic side of the infection – somewhere quite different from that ‘nothing to worry about’ place that many of us were sleepwalking through all those days ago… way back in February!

Facing the lack of political direction some countries are experiencing, it is no bad thing to take an analytical approach rather than just adopting an opinion. Opinions can be interesting, but everything makes more sense when approached from an evidence based perspective.

Are some of our leaders indulging in blue sky thinking, or is it all just a bit fluffy.

There have been three ways to go with the COVID-19 pandemic and the approach has varied from country to country.

1: Herd Immunity: Let people get infected and when a large percentage of the population has developed immunity the disease will drop away.

Several countries started out with this approach but abandoned it when rates of infection began to rise and put health services in danger of being overwhelmed. Sweden has held on to one version, but it’s less a ‘herd immunity’ policy, than a watered down version of self distancing, with children still at school, small businesses operating, and no travel restrictions. It might have worked out because Sweden has a low population, but there could be other reasons – perhaps even the cool Scandinavian approach to greeting one another has played its part; but as infections begin to rise, there is pressure building for a more rigorous approach to dealing with the virus.

2. Personal distancing, isolation of the most vulnerable, and in extreme cases a total lock down: people will still get the disease, but the infection rate will slow enough to allow medical services to cope. Britain started with 1. found it difficult to hold infection rates to manageable levels and switched to 2.

3. The South Korean and Taiwanese approach has been to combine technology with contact tracing, and use and aggressive strategy to  limit the number of infections – this works well where people can be relied upon to follow instructions, but it doesn’t work everywhere. The danger is that the population will not get a high percentage immunity and the disease will returns from outside at a later date.

Only time will tell which approach gives the best results, but there is an indication that, in the end, all will lead to a similar outcome: rates of infection will vary, and the results come at different times.  As yet, nobody knows what will happen, and there’s always a chance the disease could just run out of steam and disappear entirely, but as yet, shows no signs of doing so.  

Things we should know when thinking ourselves through the COVID-19 pandemic.

It is helpful to know what is sometimes termed ‘the percentages’ to get a better understanding of how an infection runs.  Although it doesn’t apply to all contagious diseases, a basic plan of fifths is a model applicable to many, and appears to work for COVID-19. The general rule for those infected is that four fifths will show trivial symptoms but still be contagious; one fifth will show more severe symptoms and one fifth of those with more severe symptoms will be in a serious life threatening situation.

Viral load doesn’t have so much arithmetic about it, but it is relevant, especially to medical workers. With other infective disease, it has been noticed that the first person in a family to contract a contagious disease will sometimes show less severe symptoms than others members of the family who later become infected. The suggestion is that the level of a virus contracted can increase the severity of an infection. If this story proves to be more than just anecdotal, it might explain why health workers are at such great risk, especially when intubating patients (inserting and removing a tube into the trachea to aid breathing). At such times they are subjected to high levels of the virus. This merits a mention because so many health workers have been poorly provisioned with adequate protective clothing which is entirely unacceptable, considering how long some authorities have had to prepare.

With any serious viral infection one of the most important considerations is to understand what exponential growth really means: it is a progression of numbers that double up over a period of time; this sounds easy to understand, but few people fully comprehend the consequences of this form of increasingly rapid growth. If a disease is increasing exponentially, it is possible to recognise the end game by reading the figures correctly in the early stages: essentially it is a question of identify what you are dealing by understanding the numbers. I have outlined the details of this in a previous article: ‘Take a Picture – Save the Planet. UP, UP AND AWAY. From Ebola to Exponential and Beyond.’ and all I need to say here is, that whenever you see an exponential curve and have some kind of negative relationship with it in its later stages, then ‘Be afraid. Be very afraid’… This sounds extreme, but many of the problem issues we currently face, especially those relating to the environment involve dealing with exponential growth, because when you get to the steep end of the curve things can get critical. 

Go back a few generations and consider the affects on our world of such activities as burning coal, oil use and rapidly increasing human population  –  they all looked very different when our ancestors were standing lower on the curve, well before the steep climb that typifies exponential. Back then many might have rejected ominous predictions about the future based upon the way things were looking, but somebody reading the figures correctly could have accurately predicted the problems that we are now facing. The same might be said for COVID-19, as the spread of the disease has been growing exponentially, but when the virus started out, it didn’t sit on the lower slopes for very long, but immunologist were still able to predict from a very early stage where things were heading, while many a less well informed individual, didn’t anticipate any problems.

A few quick sketches of graphs demonstrating exponential growth. The shape is a give away, they all look very similar.

One of the graphs above, shows the U.S. death rate from COVID-19 through March 2020, and another, the release of C02 into the atmosphere between 1800 to 2020: both look exactly the same but they have nothing in common, other than being examples of exponential growth. With the CO2 graph I’ve ignored figures prior to 1800, to make the similarity clearer, but we shouldn’t make a habit of ignoring data, because cherry picking is a frequent misuse of statistical analysis to re-enforce selective points of view. Here it has been done only to demonstrate the shape of a curve with no intention to deceive.

Because COVID-19 kicked off with a vengeance from absolutely nothing and there is consequently no gentle rise of the lower slope of the curve for the U.S. Covid 19 figures,  I have added  ‘A STANDARD EXPONENTIAL’ curve which is often called the hockey stick curve. This indicates a calmer foothills slope, where the signs of exponential growth can still be read and what lies ahead is easily predictable. The question is whether the problem gets  picked up and recognised as the get out of jail card it can sometimes be.

 Sadly, by the time of writing (around 5th April), deaths in Britain caused by COVID-19 began to show a progression that looks exactly like most other exponential growth curves. Go back to the 22nd March when the figures were far lower and you might not predict what was to come. Unless they were reading the numbers, and might have been surprised by the steep rise to follow. 30th March: 180/ 31st:38/ 1st April: 563/ 2nd: 569/ 4th: 708/ 5th: 621. The way things have run elsewhere that have shown similar infection rates, the likelihood is that infections and deaths will slow over the next week or so, the numbers are about to plateau but exactly when will to some degree depend on public behaviour. If people continue to stay at home and bring down infection numbers it will certainly make a longterm difference – longterm being only a couple of weeks now as we live through the new reality of virus time.

Any of us can get daily figures on this disease for almost anywhere in the world; the death rate in particular is difficult to misrepresent – although when people die outside of hospital they are not always recorded as a COVID-19 case. Certainly in the U.K. there hasn’t been widespread testing of the general population, and without that it is difficult to assess who is infected; and it skews the percentages in relation to the number of people dying (the death rate is what it is, but the infection rate is probably higher than reported); and this general lack of essential knowledge about the disease is disconcerting.

Nevertheless, predictions for the rate of COVID-19 infections have been easy to make by simply interpreting the day to day figures we do have, as any error in the records will remain constant and make it possible to extrapolate the graphs appropriately. Sadly, many elected officials ignored the finer details of the growth rate and were slow to take action, and this had an affect on the infection rate at a later stage of the disease. Either, they didn’t understand the horrors that an exponential curve represents, or they were wishful thinkers, hoping for better outcomes.

Even the most optimistic amongst us must at some stage face reality: with infection numbers doubling every three to four days it should have been obvious that infection rates would get out of hand unless there was a rapid response: which might include social distancing, self isolation, some form of treatment or a vaccine, although the latter two options are presently unavailable. It is difficult not to feel that in both the U.K. and to a greater extent the U.S., authorities were slow to recognise the exponential nature of the disease, even when they had a clear model of what was likely to occur by observing countries like Italy that were already going through a later stage of the infection. The U.S. had at least a two week jump on some of the countries in Europe, but whatever the case, many countries did not prepare adequately .

There are many examples of exponential growth that are important to us, in particular those relating to the environment, there wouldn’t be a problem if space and resources were unlimited; certainly we run our economies as if this were the case, ignoring the absolute reality that we are living in a finite world. Now we are troubled by the steep ends of so many exponential curves, with doubling times arriving so quickly and numbers so massive, the likelihood that if we can continue the way we are drastic changes with be forced upon us, and some are already suggesting that the COVID-19 pandemic is a sombre reminder of how vulnerable we are. 

We are still part of nature, but our technologies ensure that presently many of the rules that apply to other species do not apply so fully to us.

In the natural world biological systems often run in cycles with a complex web of feed back mechanisms to limit any one thing from throwing the system out of balance. Since the development of our various technologies, humans have to varying degrees been living outside of the general rules imposed by natural systems; but we can’t control everything – there are chinks in the armour of our existence and it won’t be the last time we come under attack from a micro-organisms such as COVID-19. Viruses are reasserting nature’s influence and we’re learning lessons from a simple parasitic organism we cannot see, that is benefiting enormously from our close social interactions and high population numbers, and with deadly consequences.

Immunologists have been waiting for the inevitable, and now it has arrived we should be taking advice from those who saw it coming. This we are told is a hundred year event, but immunologists know better – our lifestyles are very different from the way they were a hundred years ago. Our population, relentless consumption, and ability to travel almost anywhere in the World have combined to make us vulnerable, and if a novel virus had hands we’d be playing right into them. It should be no surprise that we are battling a pandemic; with this perhaps an indicator of the kind of wars we will be fighting in the future.

The last pandemic occurred in 1918, it was caused by a bird related H1N1 virus incorrectly named Spanish flu – and it was never cured, never seen – there were no electron-microscopes back then. This was like no flu ever experienced. In a worst case scenario, a person might feel unwell at breakfast and be dead before their evening meal, but despite its virulent nature the disease eventually burnt itself out, having infected some 500 million people, and caused some 50 million deaths. Every viral infection has its own signature: this one carried off the most youthful and healthy wherever they gathered together, with young men fighting together during the 1st World War especially vulnerable; but this terrible toll on humanity was soon to pass from collective memory. When I was a child, remembering Two World Wars was an oppressive part of life in Britain, but there was never any mention of the virulent and deadly influenza that killed many more people than had died in the First and Second World Wars put together. From an American perspective it killed more U.S. citizens than all of the wars fought by the United States through the entire 20th Century and yet we have chosen to ignore it. 

A novel disease like COVID-19 can start from a single infection, and because the new host (in this case, us) has no developed resistance, the infection rate can increase exponentially. How much slower the rate of growth would be if the virus reproduced over the same time period as we do – say 25 years per generation. If we had that kind of time we’d undoubtedly defeat such a disease in its early stages, but viruses work on a different schedule: they have places to be and a natural ability to get there shockingly fast – so we need to move fast to.

Nobody is wandering through European cities now, and without people they have become shadows of their former selves.

Once Inside the human body, infective viruses are usually in a rush to double their numbers by dividing, and this leads to our next point of arithmetic interest – infection rates, which are measures of how frequently the virus can be successfully transmitted to other individuals. With COVID-19  infections double up every three or four days, in the U.K.. It took 13 days to go from 1 death to 100. 10 days to go from 100 to 1,000. There are only 5 numbers here; usually far too few to come to a conclusion about anything, but these numbers tell us an awful lot. I could complicate the issue by claiming that after another 4 days COVID-19 had infected another 1,000 people… but that’s predictable… so I won’t bother.

The RValue

 is the Basic Reproduction Number (or Ratio). Such numbers  are usually based on models and often quite specific in their use. We might think of the Ro Number as a general measure of infection, but that’s not quite right; the Ro number cannot for example be modified by vaccines, and is mostly used as a way to ascertain if a disease is developing in a population. If the Ro value is less than 1, the disease will not be spreading because it is in decline, but above 1 the infection will be growing, and the larger the Ro value, the more difficult the disease will be to control. There are other factors when considering how fast a disease can spread, the numbers of people in a population that are vulnerable, there are many factors, but none of them stop an Ro value from being a useful indication of how an infection is spreading.

If we see an Ro figure of 2 then it is rather like watching cell division in a petri dish i.e the growth is doubling up in an exponential manner and after less than a dozen doubling ups the numbers begin to get quite large and the disease may become difficult to control. Whether or not a disease becomes a problem depends on many things, the most obvious being how a disease is spread and how frequently that occurs. Ebola had an Ro of 2 and I’ve considered this disease in a previous article. The Ro for Covid-19 has been given during its history as having values that range from 2 to 3, sometimes 4 and quite a lot in between. All we need to know is that the higher the value the bigger the problem and that ascertaining an Ro number early on is important when estimating a diseases progress.

Dispelling the ‘Don’t Worry It’s Just Like Flu’ Myth.

Unfortunately early in the outbreak Donald Trump compared coronavirus with flu, but this was misleading. In the U.S. between 5 and 20% of people can expect to get flu during the course of a year, 200,000 will become seriously ill, and up to 20,000 will die.

The death rate of seasonal flu we know is typically around 0.1%. but during the early stages of the infection in mainland China the death rate for COVID-19 was estimated at anything between 0.4 to 2.9%; and as the virus could infect between 50 to 80% of a population very quickly, and there was no vaccine or cure, the situation was potentially very serious.

On 24th March a worried Governor Andrew Cuomo said that it was coming across the U.S. like a bullet train as  N.Y. cases topped 25,000 with 200 deaths  – he didn’t use the term exponential growth, but did say the rate of infection  was doubling every 3 days. New York was Ill prepared for the onslaught and the Governor was understandably worried. You don’t need to be an epidemiologist to know the difference between seasonal flu and COVID-19, the former doesn’t put your health service into total breakdown but COVID-19 can do so in a matter of days, particularly when the infection rate is climbing the steep part of that exponential curve – and you don’t have to dither very long before experienceing the full force of the disease.

It’s a Matter of Life or Death:

This has been a time when Governments needed to interpret available information, make decisions and then act very quickly, but they haven’t always done so. Computer simulations have been of great importance in the process, but many indicators of the path that should be taken have been ignored. In the U.K. ex-government minister Phillip Lee has spoken about a computer simulation of a pandemic undertaken a few years ago in order to inform government strategy, utilising an outbreak of a virus similar to SARS. One of the results of the exercise was that it indicated, even when there were both treatments and a vaccine available, there would not be enough ventilators for the predicted number of patients. The obvious question is: why the government didn’t react to this important information? Most likely there was a belief that the chances of a SARS like pandemic was low, but when COVID-19 kicked off, why wasn’t there a more rapid reaction to the emergency? Certainly it has been shameful that very basic supplies of protective masks, goggles and clothing have been in short supply and very limited testing even of medical staff for the virus. This to most people is unacceptable; health workers on the front line need more than just a round of applause. Having witnessed the outbreak in Italy, and even earlier when the virus became a problem in China, there was time to react, but preparations for the spread of the virus were unacceptably slow.

Spring is in the northern hemisphere, and many feel they are missing on it.

In Britain there was further criticism because testing is essential for monitoring the spread of the disease and it has failed to do this adequately, even when the disease was running up the steep end of the exponential curve. Some countries have been more efficient in their dealings with the threat. Germany for example was setting up testing labs fairly early on, but Britain did not react as quickly, and put all their efforts into a single dedicated lab – this to ensure standardisation of testing, in preference to using university and other laboratories around the country that had volunteered help. The government project then had problems accessing chemical reagents required for their tests because these weren’t purchased early enough. In consequence the system hasn’t been moving fast enough to deal with even the most basic number of tests – they soon might though, as help has now been accepted from some of those other labs, but it could all be coming rather too late.

Both of these stories came out on the same day that Britain reported 563 deaths from Covid-19. It was April 1st All Fools Day – unfortunately the virus moved with great speed, but of course governments are not usually so good at doing that and the result almost certainly will be be a greater loss of life. A thoughtful person might be wondering how we will look back on this predictable situation that got very much out of hand. Maybe it just hasn’t been a fair fight – the virus has been efficient and has moved very fast, while governments in general… Well, perhaps not so much.

Now is not the time to draw too many conclusions, but at some stage, after we’ve worked out exit strategies from the present pandemic (and that’s a whole other story in itself), there will have to be questions asked. The next time a pandemic occurs, which if nothing much changes is a certainty, we must be better prepared for the fight. We owe that much at the very least to all of those who have so far lost their battle with this deadly enemy.

Next: COVID-19. Simple Arithmetic and the ‘Economy First’ Delusion. PART 2.

UP, UP AND AWAY. From Ebola to Exponential and Beyond.

Perhaps the most reliable way to ‘save the planet’ is to take a picture that has been constructed by using mathematics and arithmetic; these exist in a variety of forms, but most commonly they are represented as charts or graphs that can provide at a glance, information on any subject for which there is reliable data, and graphs in particular are good at showing numerical change against a baseline of time.

I’m one of those unfortunates who have trouble adding up a column of figures – seldom do I get the same total twice – even with a calculator! That’s discouraging, but it’s not a valid excuse to give up.  And mathematics doesn’t come any easier, but let’s face it, we owe it to the planet to try, because mathematics is the key to measuring everything important that is going on around us.

A politician or national spokesman who says, ‘I’m just hopeless with maths’ or ‘math’ (depending on where they are standing) and then laughs it off, should be looking elsewhere for work. There is understandable concern when the people who represent us do not usually have backgrounds in mathematics or science – political science doesn’t count, because that’s an oxymoron. Anyway, the ‘I don’t get mathematics’ excuse is unacceptable from any elected official and we should urge them to ‘try harder’.

When I heard a health spokesman say recently that the Ebola virus epidemic in West Africa was growing exponentially month by month there was obvious cause for concern. The spokesmen then gave the number of infections that occured during the previous month followed by the predicted figure for the month to follow, and the figures were exactly the same. This implied that he either didn’t understand exponential, or the increase wasn’t exponential at all. The statement was confusing: was the  rate of infection steady and controllable? Or was it expanding  exponentially, suggesting that  heading for the hills was the best possible option?

Understanding exponential growth shouldn’t be a problem. Most small children can draw it, even if they can’t describe the outcome.

Little Timmy can't say the word, but he can certainly draw it - a simple example of exponential growth.
Little Timmy can’t say the word, but he can draw a simple example. Here, a single person infects two others and if the disease is passed on in the same manner, the infection quickly gets out of control. This kind of growth applies to many things including human population growth.

In everyday life, most people don’t think much beyond arithmetic progressions, where the increase between numbers is constant.  But exponential growth is nothing like that. Once you start down the road to exponential, by doubling up, it isn’t long before the figures are mind blowingly large, and if they relate to a dangerous disease that goes unchecked, no health service on the planet will be able to deal with it.

There is an ancient Persian story that explains the process well. An inventor who pleased his king with a wonderful invention was asked to name his reward; but he at once disappointed the ruler with the seemingly meagreness of his choice. The inventor asked for grains of wheat to be placed upon a chess board in the following manner: one grain on the first square, two grains on the second, four on the third, eight on the fourth, 16 on the fifth and so on, until all of the 64 squares were covered. The numbers start small and most of us don’t think much beyond the 8th square where the total hits 128 grains, which isn’t an outrageous figure. Quite a surprise then to discover that to reach the 64th square requires 18,446,744,073,709,551,615 grains of wheat – more wheat than was available in the whole kingdom. The tale is spun as  an example of intelligence winning the day, or alternatively, it is a story of cunning and greed –  the inventor either becomes ruler of the kingdom, or he loses his head.

In today’s world we might relate this story to pyramid selling where an investment doubles up every move it makes down the line and before long the numbers become vast, but by then, many individuals have dropped out of the scheme and never pay their contributions, while those who stay in begin to run out of suckers to sell to.

Telling a story is a great way to explain numerical change, but an artful graphs is a more visual approach. The two graphs below are free of annotation which allows the image to pass for art if you prefer it – perhaps as a late Matisse paper collage.

This could be a late period Matisse paper collage, but we might also consider it as representing two curves on a graph running along a base line of time. curves
Consider the above as two curves on a graph with a base line (or x axis) representing the passage of time, and a vertical (or y axis) representing the numbers or the density of an animal population increasing linearly as the line progresses upwards. This colourful ‘picture’,  interpreted correctly, contains enough information to save the planet .

The upper curve begins between yellow and red but continues for the most part  between yellow and green – it starts shallow, then rises exponentially before levelling off. This forms a ‘logistic curve’ first used by Pierre Verhurst  in the mid 1800s to show natural population growth where numbers are held to an upper limit by predation and availability of resources.

The lower curve that runs at first between red and yellow and then red and green takes time to rise, but when it does the line steepens rapidly – this is exponential growth that hasn’t levelled off. The world human population presently follows this ‘run away’ curve, but without infinite resources it cannot continue to grow in this manner. In a finitely resourced world the predictable result is a sudden levelling of the curve and a plummet downwards that mirrors the up. To alleviate suffering, it makes sense to control the drop – this really is a case of the higher you go the harder the fall.  Birth rates are presently falling across the developed world, but for economic reasons the numbers are usually bolstered by immigration (O.K. there will then be fewer people somewhere else, but that doesn’t regulate the population in places where people are genuinely trying to control their numbers).

The logistic curve along with the wave curve (see the predator prey relationship graphs below) apply to almost any species other than our own and they have longterm benefits for both the species and the environment – and make better models for longterm regulation than does uncontrolled exponential growth. All the information we need for responsible behaviour is contained within a couple of simple graphs, indicating that self regulation of human population is a better option than the inevitable collapse that continued exponential growth has in store .

Unfortunately, governments do not run economies with a view to longterm sustainably – they invariably opt for growth above all else, and are reluctant to make changes, preferring instead to pass the parcel onto the next generation – a ticking time bomb which they’ve chosen to ignore. Economies are run as if resources are infinite and without cost beyond extraction, refining and transportation. However, at a certain point, the Earth will no longer be able to sustain this, and if the present generation continues to charge up the steep end of exponential… future generations will be forced to pay the price, and will know that we had all the information available to make the right decisions, but instead carried on, business as usual.

 

HERE WE ALL ARE, UP ON THE STEEPEST PART OF THE CURVE.

Human population growth started off slowly.It is obvious that population wasn't a problem prior to 1800, but an agricultural revolution, an Industrail Revolution and the development of modern medicine has aided population growth and  when the graph is climbing as it is today, there is a genuine need for us to engage with the reality.
Human population growth started off slowly. Population growth clearly wasn’t a problem prior to 1800, but an Agricultural Revolution, an Industrial Revolution and the recent development of modern medicine have all helped to allow our numbers to grow exponentially and there is now a genuine need for us to engage with reality.

Things often start off slowly before exponential growth kicks in. With the human population nothing much changed for a very long time. There was even a period around70,000 years ago (long before the time line represented in the above graph), when the human population dropped so low we almost disappeared altogether.

It may well have been cooking meat and the development of  agriculture that started things moving, but there have been other set backs: the black death was a devastating pandemic and can be seen as a dip in the population graph around 1400. Prior to the plague weather conditions around the mid-1300s  were unfavourable, and throughout Europe crops repeatedly failed. It was a perfect storm of a disaster and millions died – but the loss of a third of Europe’s population did change the economy. Suddenly, there was a shortage of workers and for the first time in recorded history a more reasonable wage could be asked by those who survived the devastation. Poverty was still widespread, but many people were liberated from serfdom, and took the first steps along a path that generations later would drive the Agricultural Revolution, the Industrial Revolution and eventually the modern Western economic system we have today.

In the broadest sense exponential growth isn’t a disaster, it is often the way things increase in the natural world, but there are always boundaries. A fertilised ova wouldn’t develop at a rapid enough rate if cell growth wasn’t initially exponential, but once a certain functional level has been reached, cells are programmed to be replaced when and where they are needed – if they keep on dividing without control, we call it cancer.

Almost everything that relates to our rapidly increasing human population is unsustainable.  The graph below demonstrates a normal predator prey relationship where foxes are eating hares; it could equally be wolves preying on deer, or any number of other predator prey interactions.

Along a base line of time the green curve of prey animals increase, producing more food for predators which set the pattern for controlling the prey as the prey numbers decline, so do the predators. The winner is plants. Without the predators the world becomes less diverse as the plants are eaten. This of course is an oversimplification as there is a web of life, but the principal holds.
Along a base line of time, the green curve shows prey animals beginning to increase in number, thus producing more food for their predators, the foxes – shown in black. Foxes then increase in number, eat more hares and cause their prey to decline. Fox numbers begin to fall in response to the diminishing food supply and hare numbers pick up again – the process continues in a cyclical manner.

Other species also benefit as predator and prey numbers ebb and flow. Plants for example will escape total obliteration by hares and rabbits as predators reduce herbivore numbers. Without natural predation environments become less diverse as certain species are eaten beyond their capacity to regenerate. However, the predator prey graph is an oversimplification, and although the general principle holds true, the system is really a three dimensional web of life that demonstrates far greater complexity. We refer to a natural balance of nature, but the reality is closer to a series of peaks and troughs. If our human population followed closer to the logistic curve, modern technology would allow us to regulate against a roller coaster of loss and gain in a manner that can’t so easily be applied to the steep end of exponential growth.

Related closely to our population numbers is the extraction and burning of fossil fuels.

This graph shows the level of oil extraction (fossil fuel) and as would be expected it follows the same line of exponential growth for the human population. Coal extraction starts a fraction earlier on the time line, but follows the same exponential growth line.
This graph shows the level of oil (a fossil fuel) extraction.  As expected it follows the same line of exponential growth shown on the human population graph. Coal extraction starts a fraction earlier on the time line, but clearly follows a similar exponential growth curve.

It is impossible for us to remove and burn fossil fuels indefinitely, because such resources are finite and as time passes, these diminish and become increasingly difficult to extract. And another consideration is the effect that burning fossil fuels has on our atmosphere should we decide to try it.

The increasing emission of carbon into the atmosphere when fossil fuels are burned is clearly changing the Earth’s atmosphere.

Not surprisingly Carbon dioxide emissions due to the burning of fossil fuels also follows an exponential line.
The time line starts here at 1600 – before this time, man’s burning of fossil fuels was negligible, but when the Industrial Revolution kicked in Carbon dioxide emissions began to pick up and were soon growing exponentially. Once again the sudden ‘up’ part of the curve runs close to the curve for human population growth.

Burning fossil fuels has a special place in the grand scheme of things, because it increases the levels of Carbon dioxide in the atmosphere and that in turn increases global temperatures. Continuing to do so at an ever increasing rate not only changes the atmosphere, it also changes the weather and at a certain point these changes may be irreversible.

Some times politicians and spokesmen do know how to use the figures in their favour. Global temperatures are evidently rising, but what if they were to show you only the section on the red box?
Some politicians and spokesmen do appear to know how to use graphs when they work in their favour. Global temperatures are clearly rising, but what if you were shown only the section of graph in the red box?

If you looked only at a graph showing the period between 1950 to 1970 you’d consider global temperatures to be fairly stable.  There has also been a similar levelling of temperatures in recent years; these are the favoured areas for climate change sceptics to cherry pick their examples and tell us, ‘there’s nothing to worry about’, but unfortunately, there can be no denying the general temperature trend is upwards – the planet is warming, which supports the idea that it is necessary to always view the whole picture.

The Ebola infection figures discussed earlier do indeed appear to be growing exponentially (at the time of writing). The curve ran fairly level through May and June, which would have been the ideal time for the developed world to have moved in and defeated the disease before it took off. To have ignored this opportunity seems careless if not arrogant. The question is, if I can manage the calculation on the back of a cigarette packet (see below), why can’t those in power do the same. It would be generous to put the terrible suffering in West Africa down purely to ignorance, but sometimes it is suffering economies rather than suffering people that elicit the most rapid responses.

Below: an ‘on the back of a cigarette packet’ calculation derived from figures freely available from news reports. This was quite tricky – not the mathematics… it’s just that I don’t smoke.

A back of a piggy packet graph for Ebola infection. Hopefully the infection will now begin to come under control - an exponential doubling month by moth is almost too horrible to contemplate.
A back of a ciggy packet graph for Ebola infection shows more than 13,500 cases at the time of writing ( I drew this graph during October. Since then the figures have rapidly picked up and I’ve had to extend the graph upwards). Hopefully the infection will now begin to come under control – an exponential doubling month by moth as can be clearly seen between the beginning of October and the beginning of November is too horrible to contemplate. Potentially, there is a long way to go before the disease peaks and crashes naturally if it is allowed to spread unhindered.

 

So far there have been around 5,000 deaths due to Ebola and there will be many more in the coming months, but hopefully, now that medical help is arriving in the affected West African countries (better late than never), the infection will begin to come under control.

Whenever we hear a spokesman say that ‘growth is exponential’ it is good to be clear about what he or she means. Certainly this is important when it refers to human population growth; or the increasing use of fossil fuels; and the rapid spread of a contagious disease. In each case we need to ask the right questions, then be certain that our answers make sense, and last but not least, act as quickly as possible – and so far we have been unforgivably slack on the last one.

The ciggy packet slip aside, all of the simple ‘mathematical’ pictures shown above have been colourful, and without exception are easy to interpret – this isn’t intended purely for the benefit of small children – it is also to grab the attention of the mathematically challenged politicians making important decisions; they really do need to, ‘get the picture, act in good time’, and in so doing, ‘save the planet’.

In mid October 2014 Tony Abbott predicted that coal would be the world’s principal energy source for decades to come. It was he said, ‘Good for humanity’. I wonder if I’m living in a parallel universe – Tony Abbott must be better informed than I am… he’s the prime minister of Australia.

At the time of posting there was some hopeful news. A decrease in the number of reported cases of Ebola in Liberia. WHO’s spokesman Bruce Aylward said the response to the virus was now gaining the upper hand, but warned the crisis wasn’t over. The Head of the U.N. Mission says that ‘presently he doesn’t have the  resources to defeat the disease’. How nuts is  that?

For a perceptive and amusing view of man’s destruction of the Planet,  take a look at this cartoon:

http://laughingsquid.com/man-animated-short-showing-our-destructive-relationship-with-earth/