By ir.Jaap van Till, 27 maart 2020. Updated: May 2.
Translated into English March 29
In recent weeks people asked me frequently: “How does the Corona Virus spread so fast?”.
I am happy that they admit so frankly they are confused about it or that it behaves so much more lethal than they could imagine.
Whole tribes of talking heads, politicians and the insistant science-TV and social media commentators had their views ready within seconds and started to confirm each other about “light cold” flu, like the Brazilian (self declared very fit) prime minister. No. the Corona Virus is not that, and I fear Brazil will face many people dying, just like the UK and the USA. Sad.
Fractal replication of the Corona Virus; by Jules Ruis
a. Well, what IS the Corona Virus. And how does it WORK once it has penetrated the body of a victim. See for a clear presentation of pictures by Jules Ruis  and a clear article (in Dutch, in Trouw) for more detailed desciption how infection and treatments work.
The virus is not living creature, but a biological structure that, making use of the foodsupply in its host environtment, attaches itsself to cells, multiplies fast, and moves to human respiratory systems, where it leads to spreading and lung congestion/ suffocation within days.
That multiplication works in a “fractal” way, which means that the virus ‘sphere with extensions’ explodes into small spheres that themselves grow into a virus structure, etc, etc. Jules Ruis, chairman of the Association “het Evoluon” in Eindhoven, made clear pictures of that, see above.
b. How does it spread
See: Why we shoud all wear the best possible masks:
And: The Chinese have invented a vastly improved mask with graphene filter layer, for
48 hours use:
c. How can Corona spread so fast, wide and over massive amounts of people ?
The insideous and staggering of any virus outbreaks is that it can jump from person to person (even children) without showing symptoms yet. And the infected can infect others without themselves knowing it. See also what happened with Ebola and SARS. And the number of infected people exhibits a very low (small number) and slowly increasing run-up at first and then (because of that) an unexpected sudden unstoppable gigantic growth. This sets uninformed politicians on the wrong foot, until it is too late.
This explosive spreading is well known by what our parents called “fads”: sudden fashion crazies, aped by the young in clothing, hairstyle, music& dancing and ….telecom and internet gadgets and technology (my field :-))
One or two brave nutcases start with something crazy and show it to their friends, who copy them and who show it to others convincing them they can not do without it in the tribe, and who infect others with the idea, etc. The Netherlands by the way is a very perfect field lab for testing new fads as is shown by the fact that many artists test their acts in Amsterdam —->NL with a large enough online and in real life population (17 million).
Imagine that each person who is infected will infect two others within a certain fixed. time. That will result in a fast growing explosion, slow at first, of
2 4 8 16 32 64 128 256 512 ……2^n . (two to the exponential power of n)
Shown: R = 2
This means it grows ‘exponential’, and it has a fixed doubling time. “It occurs when the instantaneous rate of change
of a quantity with respect to time is proportional
to the quantity itself”.
Try it out yourself on your smartphone calulator App: 2 x 2 = and then press the = about 30 about 30 times, which will result in about 16 million. This mean that if the fixed doubling time would be one day the whole population of The Netherlands would have been infected in 30 days.
The trouble with exponential curves is that different people interprete these graphs very differently. Those that are familiar with such exploding phenomena, techies like me, know that there IS NO SUDDEN ‘bend in the curve’, ‘take-off of an airplane like’, or ‘exceeding of a certain critical threshold’. That is BS because the whole curve is exponential, and you can measure the fixed doubling time, which characterizes it, from day one !!! Except that almost everybody in our society, except us nerds, has been trained to be only surprised, find a sitation impressive, newsworthy and asking for attention when it is BIG. A frightening illustration of this early under estimation is this film which shows the reaction of the USA POTUS Trump during the rizing impact of the viral disaster:
Press, the general public, politicians and managers only start to give attention when someting is sensational (big accident – usualy accompanied by the number of death & wounded). And when it grows most brains think in terms of streight lines (see above graph with “linear increases” meaning they extrapolate to judge if action is needed.
They draw an arbitrary increasing line trough the curve and YES below the crossover/takeoff point the techies have overestimated the severity of the phenomenon (“it is only a small group who will get it and it will only be a light touch of flu , will be over in no time”). And above the crossover point the “managers” have massively underestimated it (and it is then too late for governments to do anything, and maybe we can all beter disregard it – Trump and Johnson). Tragic stupidity, and maybe implemented by aliens to do an intelligence test on governments who fail to listen to their scientists. Brazil failed that and will have to pay in huge numbers of casualties.
What happened in realty, the Corona Virus outbreak was discovered in December / January 2020 because doctors detected a very aggressive/ very infectuous (viral) form of pneumonia in Wuhan (might have originated from elswhere) and within a very short time in a couple of other countries. They knew they had to sound the ALARM because of the apparent short doubling time: 1 or 2 days. With their calculator they could then show in how many days the infection would spread to infect the total human population on this planet. Try it yourself with 2X2 and then pressing the = on the screen to reach 7,000,000,000. And they tried to notify the WHO who declared it to be a Pandemic.
The exponential curves have, besides a long slow startup phase, another graphical representation problem: the explosion bursts through the paper on the right hand side upper corner, what ever scale you have choosen. Solution to this problem is to use a logarithmic scale (vertical 10 100 1000 10,000 etc.). This turns the exponential curve into a streight line. See for example the last graphic of the countries in this little story. unfortunately though this way of presenting the figures takes away the alarming message from superficial bystanders, since it looks very calming “streight line” again.
Lesson 1: In viral infectuation situations we should NOT look at the size (number) of the infected, but to the doubling time of that number. A short one like for instance 1 , 2 or 3 days means we have to face an explosion.
d. Can nothing be done to halt /slow down the spreading?
We surely can,
– if we properly protect the medical personell,
– if we measure on a large scale and
– if you are able then to reach the few infectants early and “stamp out the fuse of the bomb” just before it reaches the gunpowder. And this applies to later cases too that can be identified and isolated. Remember each infectant can start a new avalanche see the graphic above.
With Ebola and in some countries where they where able to measure people on a massive scale, they have isolated the Corona infected ones (with their family) totally and rigorously in their homes. In Wouhan the authorities even welded close front doors of infected families.
What also cab be done that the firecrackers that go off can not bring fire to the fuses of other firecrackers. And they can not fire crackers which have already gone off.
This approach is inherent in the general form of exponential growth. That will in later stages bend down the curve since infection has already taken place in most of the population that can be reached or is prevented from physical contact by limitations of movement. Then the line will bend into a maximum, a horizontal line (asymptote).
Why? Just assume that there is an outbreak of flu on a littel island, say Texel in NL. Then the spreading will be exponential until …nearly everbody has had it, nearly no more candidates to infect. The S-curve tha appears is formaly called “the Logistic Curve”, see Wikipeadia.com (this name has nothing to do with logistics, although in a certain sense ‘transport’ is also the case). See the yellow S-curve below.
This ‘logistic curve’ is defined by two parameters. A= the doubling time as mentioned, can be measured from the beginning. And B= The hight of the Ceiling which can not be crossed by the curve. By isolation of people , 1.5 meter distance, locking them up inside their house, canceling gatherings, school closures, etc. the authorities try right now to lower the ceiling of the curves.
Problem is that the bending of the curves (of fatalities, the only objective measure) from streight up to horizontal will become visible rather late in the process. And we do not know for sure yet if infections will fare up again later. We do not know!
Lesson 2. To let the viral curves bend down and get them down later, the populance must be divided drasticaly as early as possible into physically isolated groups. Only then the ceilings of the explosions will be brought down.
What i mean is the Yellow line in the graphic below, which shows the alter phases of the S-Curve after it was exponential.
Let us be happy that broadband internet is in place in most civilised countries, so we can still communicate with our family members and contine working from home. I am very proud that I helped introduce internet and digital infrastructures in Europe.
Extract from this FT graphic:
I remember that with the introduction of the ‘carphone’ the directors of the phone companies where quite happy with the rapid uptake of the devices and mobile network services. But at the same time there where internal quarrels, for intance within KPN, about how big the eventual sales figures would rize. What woudl be the ceiling (maximum candidate client size) of the market, and thus the maximunm size of the investments. How many wealthy Mercedes driving CEO’s would afford to use a car-phone? Hundreds? Now every young kid has at least two smartphones. One from every divorced parent. That ceiling had to be brought upwards again and again and its cellular network infrastructure likewise expanded. With the internet access network the same thing happened. Disbelief and lack of imagination for the fast ongoing growth of datatraffic is still not over 🙂
The Corona Virus and its spreading is [ new, very complex, non linear and dynamic ] and so it is certainly not [certain, simple, linear and static] like most things i had to learn at the Delft University of Technology in the ’60’s& 70’s plus the accompanying toolboxes we got handed as students, to calulate everything , build it , manage it and maintain it. Those days are gone. Now we have to learn, fast and cooperate on a worldwide scale.
This short story does not pretend to explain all and define steps. and actions to cope with Corona. It is only meant to hand you some knowledge and patterns to cope with the avalance of news about the outbreaks. No doctors and nurses work feverishly (SIC) to fight the disease, a number of high level institutes like the RIVM in NL and other researchers at universities analyse what is happening and work on possible cures, with models to track in detail what is happening in this compelx situation. Even dayly they are discovering clever bypasses and fractal unfoldings in nature and in the human body.
Best sources to read about that are in  and on the tweets from my friend prof. Yaneer Bar-Yam, of the Complexity Institute in Boston, see .
Unfortunately these clever and brave people have no time left to explain to the general public what they are doing in the front lines. That is why I have tried to jump into that gap and offer you here some simplified highlights.
At the same time governments have to do what they are for: do the right things at the right times, in the general interests of the population, where meny human lives are at stake. See  to read what did get wrong in the UK, what not?
Human society is going to a sudden deep transition, a systems crash that did begin in 2008. But what that transition is and what might happen in our future, I will blog to you another time.
Now we must cooperate, yes even transborder, in order to survive this virus and others.
 Yaneer Bar-Yam . Twitter: @yaneerbaryam
jaap van till, TheConnectivist
These heros are fighting for ALL of us. Respect and value them.
PS1 On April 13, somebody notified me of this German language article, also drilling deeper into what Corona Virus is, does and how it as handled in a number of countries:
PS2 On NL TV yesterday May1 Bert Slagter (TW: @bslagter) did a christal clear explanation of “exponential growth” to explain the virality of the CoronaVirus, similar to this tutorial. See: https://twitter.com/op1npo/status/1256328956644593665?s=20
He added a new term though: “exponentiele krimp” (exponential shrinkage). As i explained the total infected number will bend down due to a ceiling of candidates for infection (saturation level, see figure above) which can be lowered by isolation = drastic the cutting number of physical contacts by “lockdown”. As a result the R factor of average infected people goes down from 2 to one and if we are lucky 0.5. This results in the mirror image of exponential growth: exponential shrinkage. Instead of doubling the number of new infected each day is halved and then halved again: 40 -> 20->10 -> 5 -> 2 ->1->0 ! But beware: if conditions of contact between people are eased to early, each infected person can start a new Pandemie 😦 But we can prevent that by continued testing, tracking the contacts and isolation of the infected.