Pedagogical proposal for the development of an epidemiological mathematical model: an HIV/AIDS model as an example

Abstract

This paper an example of how to use a pedagog- ical tool of literary analysis for the elaboration of a mathematical model of HIV/AIDS is presented. For this objective, different epidemiological mod- els were reviewed to interpret mathematically and biologically the dynamics of the Human Im- munodeficiency Virus HIV and the subsequent Acquired Immune Deficiency Syndrome AIDS, a representative sample of scientific research de- veloped in the period from January 2012 to April 2019 was used, main modeling characteristics were identified as recruitment form, force of in- fection, hypothesis to be modeled and mortality. Among its main results is the elaboration of a completely original model of Ordinary Differen- tial Equations that govern the dynamics of the model and that are in accordance with the main advances of the present time, improving some of the classical forms of mathematical modeling. We conclude that the methodology used in this work is a fundamental pedagogical step in the process of starting a scientific research.