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Friday, April 23, 2021
Saturday, February 27, 2021

Mathematics and Covid-19



Havana, Feb 27.- Mathematics is the alphabet with which God has written the Universe, said Galileo Galilei; and during the Covid-19 it seems that the ink of this science signed marriage papers with the pandemic.

In charge of the curves, the pandemic peaks, and of trying to predict the number of beds for the sick, seriously ill and critically ill, Mathematics became an inseparable companion of the course of illness throughout the world.

In Cuba it is no different and every week it is common to hear names such as Raúl Guinovart, dean of the Faculty of this specialty and Computing at the University of Havana, who guides a team of experts who participate in the temporary group to confront the pandemic.

However, Covid-19 has not been the only disease in the country with which Mathematics established unbreakable links.

The story has other antecedents and about them, Prensa Latina spoke exclusively with Professor Aymée Marrero Severo, PhD in Sciences and in charge of directing the Biomathematical Modeling Research Group.

“Mathematically modeling contagious diseases makes it possible to represent the transmission dynamics, study and estimate the parameters that characterize it; and when solving these models data are obtained on the number of patients at each instant of time and other parameters of interest”.

He pointed out that, from the year 2000 and as a result of the friendship between the researchers Jorge Pérez at that time, Head of the System of Attention and Control of HIV / AIDS in Cuba and the professor of the Faculty of Mathematics, Dr. Héctor de Arazoza, conceived by the Biomathematical Modeling Group.

In this way, joint work with the Pedro Kouríen Institute began a strategy for the detection of seropositives in the country, which was essentially based on the search for partners (contacttracing in English), known today as epidemiological spider, Marrero points out.

Since then, diverse investigations began, some deserving of international awards for the results on HIV / AIDS; and others on Dengue, Zika, and studies on the cellular transmission of cancer.

At that time, most of those results remained in the academy without achieving a real impact on the management of health and disease control institutions, recalls the professor.

With the arrival of Covid-19, the panorama changed, the professor points out, and we mobilized naturally and spontaneously, to work on the transmission and control models of Covid-19, already with the publicly recognized results.

Numerical models of a pandemic

During the pandemic, the most widely used models (although not the only ones) are the so-called population epidemiological models, which subdivide the total population into classes of research interest, explains Marrero.

The simplest of them considers the subpopulations of susceptible, infected and recovered or removed, but there are other variants that allow defining, in addition, the classes of asymptomatic, latent or exposed, in quarantine, among others.

Said models essentially defined by ordinary differential equations make it possible to simulate how the number of individuals in each of these subpopulations varies over time; as well as the rates of infections, latency, recovery and death, among others.

Referring to one of the models in which she has worked, the professor explains that “the subpopulation of active infected, diagnosed with tests and tests for the SARS-CoV-2 virus and that of recovered are the only ones under the control of health entities and community, either in hospitals, isolation centers or under enforcement in their homes.

This type of modeling allows making a diagram of nodes (vertices) that represent the different subpopulations and edges that connect these nodes, on which the parameters that characterize the transition from one to another are written.

 

According to Marrero, Mathematics and Computing have endless tools, methods, possibilities to study, analyze, simulate, monitor and predict practically all the phenomena of life.

Valuable results demonstrate this and can influence a better understanding of these phenomena and therefore better organization and control. What happened with Covid-19 is the best school to know how to articulate and proceed in the future, says the expert.

“Using a mathematical term, I would say that the pandemic in Cuba, thanks to the interest of the Ministry of Public Health, the Government and the linking of the results of the different spheres of science, especially medicine, biotechnology, virology, epidemiology, mathematics, computing, among many others, could be classified as: LIMITED”.

In Mathematics this concept refers to a situation in which for a certain object of that branch or another one built from it, an order relationship can be established with another type of entity called upper or lower bound.

 

Mathematics and pandemics, millennial union

Mathematics possesses not only the truth, but a certain supreme beauty. A cold and austere beauty, like that of a sculpture ', expressed the British philosopher, mathematician and writer, Bertrand Russell.

An article in the Spanish Newspaper El País reviews some of the advances in this numerical science that emerged in times of pandemics.

"In fourteenth-century England, mathematical advance was mainly due to the so-called 'Merton calculators', a group of schoolchildren linked to the Oxford MertonCollege. The main calculators were the British Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton.

Bradwardine - who was Archbishop of Canterbury - anticipated the notion of exponential growth, by extending the theory of proportions from Eudoxus of Knidos.

Exponential growth is an increment that grows faster and faster as you advance, for example, an amount x that doubles in each time interval; Before long, in n steps, it will have grown prodigiously to (2 ^ n) x.

That is what happens in an epidemic with infected people or in a culture of bacteria.

Another great scientist in history who made great contributions to mechanics, gravitation and laid the foundations of the differential calculus was Isaac Newton.

Current mathematical models of epidemics are mainly based on differential equations that dictate the evolution of the contingents of susceptible, infected and recovered from the notion of derivative.

In 1927, the biochemist William OgilvyKermack and the physician epidemiologist Anderson Gray McKendrick, both Scots, developed the so-called SIR model, which is still used to model infectious disease epidemics.

The acronyms have the following meanings: 'S' for susceptible, 'I' for infected and 'R' for recovered.

On these models, the journal Nature published an article in which it makes reference to other related models.

Among them, the SIRS in which the last 'S' is once again the word "susceptible", and means that, unlike the previous one, the recovered person does not obtain total immunity, but decreases over time until returning to be susceptible to infection.

Despite its complexity, "unfortunately even the most detailed and realistic of mathematical models is not able to predict when the current pandemic will be brought under control," wrote Christian Yates, professor of mathematical biology at the University of Bath, UK, citing the BBC network.

Numbers are a universal language. Counting, taking accounts, defining how much it can weigh, be worth or last has always been a constant in humanity. Mathematics is a science that does not cure directly, but helps results.

It was the French philosopher and mathematician René Descartes (1596-1650) who asserted that this is the science of order and measure, of beautiful chains of reasoning, all simple and easy. (PL)