Physical exercise and strengthening of immunity. Mathematical mode 41
Resumen
En el presente trabajo se analiza c´omo los ejercicios f´ısicos pueden influir en el aumento
de la inmunidad de una persona; se realiza un estudio de los diferentes tipos de pat´ogenos, en
particular se investigan las caracter´ısticas de los virus, sus manifestaciones y apariencia; se
estudian las caracter´ısticas del sistema inmunol´ogico as´ı como la inmunidad, ya sea innata o
adquirida. Se investiga la relaci´on entre los virus y el sistema inmunol´ogico de una persona,
as´ı como el sistema inmunol´ogico puede reaccionar ante la presencia de un virus.
La din´amica de la interacci´on del virus vs el sistema inmunol´ogico se simula mediante
un sistema de ecuaciones diferenciales ordinarias, se determinan los puntos de equilibrio y el
comportamiento de las trayectorias en una vecindad de las posiciones de equilibrio, adicio-
nalmente se estudia el caso cr´ıtico de un autovalor cero y uno negativo, dando conclusiones
sobre el proceso en los diferentes casos.
Palabras y frases clave: Modelo matem´atico, epidemia, ejercicios f´ısicos, immunidad.
1 Introduction
The immune system is a set of elements that exist in the human body. These elements interact
with each other and are intended to defend the body from diseases, viruses, bacteria, microbes,
among others. The human immune system serves as a protection, shield or barrier that protects
us from undesirable beings, antigens, that try to invade our body. Therefore, it represents the
defense of the human body.
There are confessions of patients who, due to the doctor’s suggestions, permanently started to
perform physical exercises to strengthen their immune system, in the face of infectious diseases,
perceiving a low immunity; gradually obtaining a change in your organism. The fitness coach
stated that he was not the only case, as he had others with similar situations. This problem is
addressed further in specialized bibliographies (cf. [1, 2, 14]).
When the immune system does not function properly, it decreases its ability to defend our
body. Thus, we are more vulnerable to diseases such as tonsillitis or stomatitis, candidiasis, skin
infections, ear infections, herpes, colds and flu. To strengthen the immune system and avoid
problems with low immunity, special attention is needed with food. Some fruits help increase
immunity, such as apples, oranges and kiwis, which are citrus fruits. The intake of omega 3 is
also an ally for the immune system.
The immune system is made up of a complex of different cells that receive and emit different
signals directed at white blood cells, thus regulating the body’s defense mechanisms. The me-
diators of this interaction are proteins, peptides and other substances that for their activity are
called immunomodulators. Biological immunomodulators are made up of a group of molecules
with specific properties, many of them chemically and biologically very well characterized and
others to be discovered. (cf. [16,18]).
In the human organism there are own cells and inappropriate cells, among the inappropriate
are pathogens; These inappropriate cells can cause changes in the body, which can turn into
diseases and even cause the death of the person; pathogens can include viruses, bacteria, fungi,
and parasites; these can be intracellular or extracellular.
Viruses are simple structures, they are considered mandatory intracellular parasites, because
they depend on cells to multiply. Outside the intracellular environment, viruses are inert. How-
ever, once inside the cell, the replication capacity of viruses is surprising: a single virus is capable
of multiplying, in a few hours, thousands of new viruses. Viruses are capable of infecting living
Divulgaciones Matem´aticas Vol. 22, No. 1 (2021), pp. 40–51