Coronavirus: contagion math to keep calm in the midst of chaos

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The mathematics of contagion is simple. As simple as crucial. Now that we have learned to wash our hands properly, we move on to phase two, which comes with surprise: mathematics . If we give up the effort, we run the risk of not understanding what all this is happening to us, and that ends with an unfortunate being carried away by an often unfounded panic.

To start, let's divide into three groups. A secret of mathematics is never to go too far for the subtle, and coronavirus mathematics distinguishes the population, all of us, in an approximate way: there are the Susceptible (S) , the people who could become infected; the Infected (I) , those who have already been infected; and the healed or Recovered (R) , who are those who became infected, have overcome the disease and now no longer transmit the virus.

Each of us is able to recognize each other instantly in one of these categories, whose initials form the name of the model that epidemiologists have used in recent weeks as an oracle: the SIR model . The end.

Ok, no, we haven't really reached the end. We need at least another concept. Within the SIR model, within the heart of each infection, a different number is hidden for each disease. In recent days it has emerged here and there in discussions and articles. It is conventionally known as R0, "erre sub cero" , and its meaning is easy to interpret: R0 is the number of people who, on average, each infected individual infects in turn.

Coronavirus: R0 of 2.5

For measles, for example, R0 is estimated at around 15. That is, during an outbreak of measles, an infected person infects an average of another 15, if none is vaccinated. For mumps, R0 is approximately 10. For our coronavirus, the estimate of R0 is around 2.5 . Here someone will immediately jump to the conclusions and stop reading: "Hooray! It's low! To hell with math!" Not exactly, wait. The Spanish flu of 1918, had an R0 of about 2.1 . And we've all heard of her.

But for now we do not want to hurry to determine if the "erre sub cero" of the coronavirus is high or low. First we want to know what happens when R0 is less than 1 . If each infected does not infect at least one other person, the spread stops on its own. The disease is a fire, an empty outbreak. If, on the contrary, R0 is greater than 1 , even slightly, we are in the presence of an epidemic principle .

To visualize it, just imagine that those infected are marbles . A solitary marble is thrown, the infamous patient zero , and hits two more. Each of them affects two more, which in turn affect two more each. And so on. It is what is called exponential growth, and it is the beginning of any epidemic.

In the first phase more and more people become infected and faster and faster. The speed depends on the size of R0 and another fundamental variable of this transparent and decisive mathematics: the average time that elapses between the moment a person is infected and the moment that same person infects another . That time window, in the case of Covid-19 , is estimated at around seven days .

Here yes: end, really. Once this little information is absorbed, we can summarize all the institutional efforts, all the "draconian" measures, the quarantines, the closing of schools and theaters and museums, the empty streets, in a single mathematical intention: to reduce the value of R0 . This is what we are doing with great pain and sacrifice. Because when R0 falls, the expansion slows down. And when R0 is carefully carried below the critical value of 1, the diffusion begins to stop. From that moment on, it is the epidemic itself that suffocates. The people, not anymore.

How exaggerated!

In recent days a failure has opened between those who humbly accept what is arranged from above and those who claim that it is an exaggeration, madness, a "collective psychosis." Or maybe they don't even yell at him, but he adopts a more derogatory, more intellectual attitude, as if they said: "Go fools, let themselves be fooled," which is basically the same.

This type of skepticism is transversal, it does not depend on the level of education or on the origin or age; well, maybe of age a little yes: adult-adults seem particularly inclined. In any case, it is a human attitude and is particularly fashionable in our time. But who insists that the established exceptional containment is "exaggerated" has not understood the mathematics. Or has misrepresented them.

A common misunderstanding, for example, arises from the proposed comparison with seasonal flu. What unites Covid-19 with seasonal flu is the form of infection: it occurs through the exchange of drops thrown into the air through sneezing and coughing.

And there are general symptoms, of course, that are similar, a confusion that caused delays in the initial containment and some unpleasant accidents such as that of the Codogno hospital [which Italian Prime Minister Giuseppe Conte has accused of being at the source of the outbreak]. But at the moment there is no evidence that the coronavirus has an autonomous seasonal peak and then backs off, like ordinary flu.

Regarding the peak of infections , they have also been deceiving us with the news that in China it has already been overcome, and that it will soon reach us too. It is the incorrect interpretation of a data. It would be more correct to say that "one" peak, the first, has been reached and exceeded in China.

This happened precisely and exclusively because of its hyper-restrictive measures, that is, blocking a few hundred million people in their homes , but not because of an intrinsic characteristic of the disease. In short, R0, in China and later in the rest of the world, has been dragged by force. And now it is kept under force, as if all, obeying the institutions, were pressing the lid of a pot full of boiling water.

Mind you, if the measures were relaxed, in China and in Europe, the R0 would probably return to its "natural" value of 2.5. The contagion would begin to spread exponentially. Epidemiologists know that the only way to really stop an epidemic is that the number of Susceptibles is low enough to make contagion unlikely .

For example when the population is vaccinated. Vaccines make us change from Susceptible to Recovered without even going through the disease. But this is not the case at the moment. The Covid-19 is still too new for us humans.

He jumped from a bat to another animal, perhaps a snake, and there the two genetic codes mixed in an unfortunate way; and from that second guest he made another leap to man, like an asteroid that throws an unknown chemical element to Earth. We have no effective antibodies and we have no vaccines. We don't even have statistics. Translated to the SIR model, it means that we are still all susceptible.

Math test question: "How many Susceptibles does Covid-19 have today?" Answer: "Something over seven billion."

Weather forecast

Another common aberration concerns the fury of the media about the "zero patient" in Italy . Patient Zero is a perfect title for a dystopian Netflix series or for a zombie movie, in fact it already exists. But the zero Italian patient has been of almost zero interest to epidemiologists for days.

From that point of phantom origin, the secondary and tertiary lines have already branched out, silent paths of contagion, many of which are probably latent. In Florence, in Liguria, in Germany, in the United States, who knows where.

And finally, there is the algebra of danger , which is also misleading. We divide the number of deaths by the number of outbreaks: zero point zero something. Translated: "You will not die!" Meanwhile, virologists leave their throat repeating that the real problem is another. The hospitalization rate required for Covid-19 is, in fact, quite high .

If all or most Susceptibles become infected too quickly, our health system would receive a dangerous collision. We would not have the necessary resources to adequately face such eventuality. We would go crazy.

The "exaggerated" actions taken by China first, then Italy, are based on scenarios that are also mathematical. Not in rumors, not in vague impressions, nor in collective hysteria. Alessandro Vespignani , who develops these scenarios at Northwestern University in Boston , told me: "It's like the weather forecast."

The basis of the simulations is the simple SIR model that we have described, but the theory applies to the real situation of our planet, of our society. All available data is used to feed the model with reality: NASA satellite maps, flight routes and the number of its passengers, information on each measurable human interaction and even certain psychological corrective measures, such as fear. Here is an area where Big Data is used to save our lives.

The simulations, once launched, show how the epidemic will develop in the next few days within certain margins of error, if it will become a pandemic or disappear. From these analyzes come the decisions of the governments. Let you raise your hand now who does not believe the weather forecast, who plans a beach vacation for tomorrow knowing that El Tiempo gives 90% chance of flooding.

Susceptible and Suspicious

Here is a curious fact: the dissemination of false news is well described by the same SIR models used for epidemics. Even with regard to fake news , each of us belongs to one of the three sets: the Susceptible, the Infected or the Recovered. Too bad that in this case we have many more difficulties to choose the right place. Often, being susceptible to the false is tantamount to suspecting the truth. The effort to accept that something radically new and "out of the ordinary" is happening is another deeply human trait of our psyche.

A form of reluctance towards the unexpected, towards the disconcerting and, above all, towards the complex, is what has taken us to take decades to accept climate change. A similar defensive mechanism develops today against the coronavirus . We don't have antibodies against Covid-19 , but we have them against everything that baffles us. It is a paradox of our time: as reality becomes increasingly complex, we become increasingly refractory to complexity.

And yet, what is happening these days is not really unheard of. "In Singapore, the government and health officials worked together to prevent the spread of infection. Draconian measures were implemented not only in hospitals: mandatory quarantine for all suspected cases, fines and convictions for those who did not respect isolation , closing a large market, closing schools, periodic temperature controls for all taxi drivers. And so the epidemic was domesticated . "

It seems he is saying it today, but David Quammen talked about what happened in 2003 with the SARS . It describes measures identical to those adopted in the Italian area of Lodi , with the only difference in the severity of criminal penalties, because our system is based on trust in citizens, on the axiom of their full collaboration.

Spillover , Quammen's book, deserves an article in itself. Suffice it to say here that it is the best way to understand the various facets of the complexity of this epidemic. Do not live it as if it were a strange exception or a divine scourge. Relate it to other ecological disasters of our time, such as deforestation, the elimination of ecosystems, globalization and climate change itself. Even entering the mind of the virus, deciphering its strategies, understanding why the human species has become so greedy for every circulating pathogen.

Sometimes Spillover is scary, it is true, there is the black bat on the cover, and sometimes it even makes you jump, for example when you ask, in 2012, if the next Big One , the next great epidemic expected by experts, the it will cause a virus that will appear "in a market of a city in southern China." Prediction? No. Only science. And a little history. It is strange that Spillover is not sold out in stores, such as antiseptic gels and masks.

According to the criteria of The Trust Project

• Coronavirus
• Covid 19
• Pneumonia
• Respiratory diseases
• Diseases
• Science and Health

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