Modelagem Matemática de Crescimento e Epidemiologia: Aspectos Educacionais

Abstract

In this work we seek to bring ideas from the theme of modeling to make a connection between the theory learned in the classroom and the real world. There was a concern to explain all the steps carefully, showing that the content and concepts covered in the modeling can be passed on in a simple way and thus point out a way for teachers to apply in high school or higher classrooms. We also leave suggestions on how to make an application in the classroom, enumerating steps that can be followed or taken as a basis to guide students during the process of formulating theories and equations regarding the phenomenon to be modeled. Based on current events in the year 2020, where there is a great concern with the contamination and spread of the new corona virus (Sars-Cov- 2), this work seeks to focus on the main models of growth and epidemiology to describe, study and teach about the reality we live in. Explanations about exponential functions and geometric progressions are also covered with examples focused on the theme of exponential growth of viruses. It is expected that, as well as the ideas about modeling, the examples of exponential functions and geometric progressions will also be applied in the classroom in order to contextualize the teaching of mathematics using a theme that has had a great impact on the lives of people across the world. world. Algebraic and numerical methods were used to solve the di erential equations present in the models. In educational terms, the nite di erence method (MDF) was introduced in order to promote the discretization of the continuous model, thus bypassing the theme of ordinary di erential equations, which is inappropriate for high school and in the rst periods of graduation. Discretized models can be solved by MDF in a simple way, using only Excel spreadsheets, whose explanation for creating them was described step by step. The proposed methods can be applied to other types of models, varying as needed. We believe in the idea that teaching methods should cover, whenever possible, a daily context in order to show the possible applicability of certain content in his life, bringing to the student's daily life what was learned in the school environment