Abstracts Mathematics

Análise de modelos epidemiológicos e evolução

by José MARQUES NETO

Biomathematics has biology as an object of study through modeling and mathematical techniques. Although mathematics as a human science has already emerged in an applied form, humanity only began to use it to study the life sciences in the modern age, with Fibonacci. Since then, we have had a significant increase in knowledge in this area, so that today we can study evolution, epidemics, demography and ecology using the science of numbers. The study of biological evolution can be done, for example, through models that use population genetics or through the analysis of the invasion of a mutant gene to a population in genetic equilibrium. Epidemics can be studied using compartmentalized models that use the letters S, E, I or R, only presented to humanity in the twentieth century. These models gained much prominence with the discovery of the Human Immunodeficiency Virus (HIV) and the COVID-19 pandemic that began in 2020, being fundamental for the elaboration of public policies to control these diseases. Currently, we can not only study infectious diseases with compartmentalized models, but also the incidence of heart attack, diabetes and other chronic diseases. This text aims to present some population, demographic, epidemiological and evolutionary models in biomath-ematics. The Exponential and Logistic regression population models are presented and then applied to population genetics.Evolutionary dynamics are planned in this monograph throughequilibrium invasion models. Finally, population genetics is applied to a compartmentalized epidemiological model in order to predict parasitic evolution.