The Daily Prosper
Mathematical pills that improve our health

The mathematics that help improve your health

Mathematics supports medical research, providing tools to study illnesses, manage their spread and develop treatments. It also helps us to live better and have a healthier life. 


Mathematics, that abstract science that is feared by many, appears in the most unexpected places. It’s enough to look around ourselves to see the infinite number of processes and practical applications in which it has a place.

If you didn’t like equations and statistics at school, you may find you like them a little more when you know that they are beneficial to our health and they help us to live better: they foresee illnesses, predict their consequences and help in the development of medicines and treatments.

For this reason there are many people who assure us that mathematics is the future of medicine, and here we recount some of the uses that it already has in the sanitation field and in that of health.
 

A differential equation to save everyone

It is estimated that there are 71 million people in the world who suffer from hepatitis C, according to data from the World Health Organisation. This illness, which literally means inflammation of the liver, is caused by a virus that is transmitted through the blood and that can carry with it serious risks, such as cirrhosis or liver cancer.

The cure rate depends on several factors, but in recent years it has improved enormously and it is already at 95% thanks to improvements in medicines. One of the guilty parties for this encouraging percentage is an equation.

Mathematical models and differential equations helped the developers of the revolutionary drug to make the discovery and to fine tune the research. Molecular biology and medicine were supported by mathematics to analyse the behaviour of the virus when the medication was administered to the patient. Aside from controversy about the price of the medication, the mathematical observation of the patient’s immune system smoothed the way to the cure.
 

Get vaccinated! You don’t want to spread an epidemic

We see it at the cinema: at the most unexpected moment, an epidemic outbreak could make the world implode and, who knows, lead to a zombie apocalypse. In more street level scenarios, the reality is that, faced with an epidemic, we need not only the relevant sanitary measures, but also to assess the probability of its propagation.

So the percentage of people who must be vaccinated in order to avoid a global pandemic is calculated. For example, in the case of measles, it should be approximately 92% of the population  so that the remaining people are not at risk, something that is known as flock immunity.

As the mathematicians Clara Grima and Enrique F. Borja recount in their book Las matemáticas vigilan tu salud (Mathematics are watching over your health), this is a powerful tool that enables us to understand the spread of a disease and how to put the brakes on it. Some of the branches of mathematics that explain how an infectious epidemic emerges are differential equations, graph theory and game theory. They also explain how that epidemic develops and how to manage it. You already know it: mathematics also says that you should not avoid getting vaccinated.
 

Mathematical modelling against cancer

There is no magic equation that cures cancer, as has been announced on other occasions, but there is a great deal of progress being made in that direction. Mathematical modelling (representing processes from the real world in mathematical language) can be used to simulate how a tumour grows and what effect a given therapy will have on a patient, as they are doing in the Mathematical Oncology Laboratory of the Castilla-La Mancha University.

This is something extremely complex due to the hundreds of different types of cancer that exist and that these researchers are already using to research glioblastoma and brain metastasis. For example, with its predictions a neurosurgeon can decide whether they need to remove more or less tumour mass.

At the University of Cádiz they are also trying to fight infant cancers with mathematics. The Recaída 0 project wants to ensure that the percentage of children who survive lymphoblastic leukaemia reaches 100%, as compared to the current 80%. How? With a mathematical model fed by data that permits the identification of new biological markers with which it is possible to redefine the risk groups among patients, predict possible relapses and achieve a complete cure.
 

If you have data, you have treasure

As in the previous examples, it is of very great value to have information about patients and prior data on the illness. At the University of Córdoba and the Reina Sofía de Córdoba Hospital they know this, and with them they have wanted to answer a crucial question in medicine: what is compatibility between a donor and the receiver of an organ?

With their new model, they have increased from 80% to 92% the probability of success in liver transplants. To do this they have used artificial intelligence, neural networks and computing and now, thanks to an analysis that cross-references all of the data, a computer is capable of assigning the donated organ to the recipient who is going to accept it best.

Another project, Sanitas Data Salud, is also trying to make good use of big data and wants to drive health research based on data to diagnose the state of health in Spain, detect trends and produce predictive models that contribute to advances in medicine. Their first study established a correlation between visits to A&E for respiratory problems and atmospheric pollution in Madrid (Spain), one of the cities that most exceeds established levels in Europe.
 

Pharmaceutical equations

When doctors hand out a prescription, they are also using mathematical calculations. Behind the recommended dosages are studies that determine the quantity of a given medication that a particular individual should take. In order to calculate this, specific mathematical equations, proportions and rules of three are used, which sometimes depend on the weight of a patient and on other factors such as gender and age.

Before the medication arrives at the pharmacy, mathematics has also been involved in its production. In laboratories, experiments are designed based on statistical criteria, and computational and data processing techniques are applied.

With these clinical analyses the dosage of the various components that each drug should include is calculated, how the drug will react in the organism is studied, potential patients are detected and, in order for the medication to be marketed, confidence intervals between which the results of trials should be are obtained. If you want to be the best pharmacist, don’t skip your maths classes.
 

To be healthy, do (mental) sport

But for everything that you have just read to worry you as little as possible, the ideal solution is to have a healthy and balanced lifestyle in which you give priority to sport, good food and mathematics! There are many disciplines in which maths is present, and there is much mathematical advice that could improve your sporting abilities. For example, there is a mathematical equation that estimates at what speed you should run and how many carbohydrates you should ingest so that you don’t faint during a marathon.

Health also comes from within, and we can (and should) feed our brain with mathematics. Brain training helps to delay cognitive problems associated with ageing, and a perfect exercise for this is mental arithmetic. Leave the calculator to one side and review the month’s bills out loud. Another way to keep our neurons fit is by doing mathematical games, such as sudoku or magic squares.

Ultimately, mathematics is not just about equations and calculations. Together with other disciplines, it can lead to notable advances that have beneficial repercussions for everybody, including for our health. Next time you hear someone protesting that they hate maths, remember that its applications in our day-to-day lives are more essential than you think. If even so they’re still giving you a headache, get to the pharmacy for a good mathematical pill. Just the one won’t do any harm.

By Patricia Ruiz Guevara