Chess and mathematics to optimize confinement measures

In 'The Seventh Seal', Max Von Sydow was looking for a really difficult enemy to beat: death itself.

During another pandemic, many centuries ago, a medieval knight risked his life in a game of chess against death.

This is how Ingmar Bergman represented the constant struggle of intelligence against adversity in his legendary film

.

Today, to win the game, Covid 19 is forcing us to apply social distancing strategies and maintain the mental strength of elite athletes.

These measures entail collateral damage, or costs, not only in economic terms, but also in social or mental health terms, among others.

The recent development of mathematical and computational methods has made Bergman's allegory real and, following an approach similar to that used to play chess, it is possible to obtain optimal policies to combat COVID-19 with the least possible damage.

Finding out what are the rules that, as a society, we want to accept to achieve a balance between cost and safety is not easy.

In other areas of life, such as road safety, a similar dilemma appears: one can eliminate traffic accidents by prohibiting driving, but this is not considered optimal due to the high social cost.

For this reason, and since the North American state of Connecticut imposed the first speed limit of 25 kilometers per hour on cars in 1901, traffic laws have been introduced, which today have wide social acceptance.

Unfortunately in the case of covid 19 we do not have a hundred years;

we need urgent and objective solutions that, although imperfect, improve the merely intuitive or subjective ones.

Here, theory beats practice: it is faster.

The models designed by epidemiologists allow creating theories and computer simulations to understand the impact of various restrictive measures on the spread and mortality of the virus, without having to wait a century.

Based on these approaches, at the University of Toronto (Canada) we have developed a model, at the request of the Government's commission of experts, that helps control the spread of the virus with social distancing measures, but also incorporates the socioeconomic consequences of the lockdown.

The objective is to find a balance between infections and costs, which adds to the difficulty of having good forecasts the additional variable of costs.

But in mathematics, the concept of "difficulty" is relative.

The key lies in the concept of

used in financial contexts by Harry Markowitz and Robert Merton, which earned them the Nobel Prize in Economics in 1990 and 1997 respectively

This idea is applied to control the autopilot of an airplane or to automate a chess game and it is also possible to do it to manage the current pandemic.

In its mathematical expression, one begins with a series of rules (those for the transmission of the virus) and a series of decision elements (public health policies, which in our case are five) and that will change with a certain frequency (in our case). model, the containment policies are updated every day) depending on future circumstances, either by the movement of the virus in the case of COVID-19, or by the movements of the opposite, in the case of chess.

As in most facets of life, brute force is useless, and one must use efficient methods, which with a few million simulations, offer a good idea of ​​the impact, costs and optimal policies

The result is a function, a computer algorithm, that allows you to simulate possible policies and see their future impact.

In principle, it would be enough to produce all the possible combinations and see which is the best.

But, as in the case of chess, they are too high, even for modern computers.

As in most facets of life, brute force is useless, and you have to use efficient methods, which with a few million simulations give a good idea of ​​the impact, costs and optimal policies.

This is

, mathematics that has been developed over the last hundred years and gave rise to the IBM

, which he lost against Kasparov in 1996, but beat him in the second game in 1997. In the fight against the virus, the method promises.

The first results that are being obtained show that the optimal movements are high precision strategies (such as the automatic piloting of an airplane) that allow to define precise policies at the local level.

As in the case of chess, there are gambits and sacrifices, such as the recommendation to close bars but not schools, during certain periods of time with the castling of financial aid to certain businesses.

Most containment policies can be improved to reduce the cost with a similar loss ratio or, conversely, to improve the loss ratio while maintaining the cost, or even improving both

It also offers surprising conclusions: although it might seem that any policy of confinement is the result of a struggle between those who want to contain contagion with containment policies and those who are inclined by economic or social considerations by proposing more liberal measures, it turns out that it is not. .

What is certain is that the majority of containment policies can be improved to reduce the cost with a similar accident rate or, conversely, to improve the accident rate while maintaining the cost, or even improving both;

This leads to the concept of optimal policies

which are computable and are precisely the ones that governments must implement, bearing in mind that they will have to be rectified as future conditions arise.

In other words, one of the consequences of the model is that the collaboration between the two positions described, and not the confrontation, produces optimal results.

Richard Feynman, another Nobel laureate, this time in Physics, said that the success of science lies in the fact that the

equations have the

solutions.

It is the essence of mathematics and its theorems: they offer universal truths that are valid as long as their conditions are met, and that are just as good for playing chess as they are for fighting COVID-19.

Luis Seco

Café y Teoremas

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