Banca de DEFESA: MARCOS EDUARDO CANDIDO DOS SANTOS

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE : MARCOS EDUARDO CANDIDO DOS SANTOS
DATA : 29/10/2021
HORA: 14:00
LOCAL: Sinop - Online
TÍTULO:

MATHEMATICAL MODEL TO ASSESS AND UNVEIL THE CASE OF COVID-19'S EPIDEMIOLOGY IN HIGH SCHOOL

PALAVRAS-CHAVES:

Mathematical Modeling; SIR model; Covid-19

PÁGINAS: 115
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
RESUMO:

This work is linked to the Professional Master's Program in Mathematics in National Network – PROFMAT of the University of the State of Mato Grosso – UNEMAT, University Campus of Sinop, and aimed to understand how mathematical modeling is used in the study and description of the advancement of Covid-19 pandemic in Mato Grosso using the SIR model. This research sought to answer the following questions: how is the study of the dynamics of infectious diseases carried out using the SIR model? How to transpose the understanding of the SIR model and the infection dynamics caused by Covid-19 to high school students? To help reflect on these issues, the theoretical framework assumed includes notions about Mathematical Modeling and mathematical models based on authors such as Rodney Carlos Bassanezi, Maria Salett Biembengut, Jonei Cerqueira Barbosa, Dionísio Burak, João Frederico da Costa Azevedo Meyer, and many others; with an emphasis on the description of the modeling process, as well as on the strategies and difficulties in its adoption as a teaching methodology. In addition, part of the theoretical framework was intended to elucidate some concepts involving rate of change and differential equations, aiming to support the methods adopted in the study process of the SIR model and based on the contributions of Rodney Carlos Bassanezi and Wilson Castro Ferreira Junior, William E. Boyce and Richard C. DiPrima, James Stewart, among other authors. The research had a quali-quantitative approach being forwarded through a descriptive-explanatory study. The research object was the Covid-19 dynamics in Mato Grosso until the end of January 2021 and the data were collected from the interactive panel provided by the Mato Grosso State Health Department - SES/MT, which were organized in Excel spreadsheets. To model the data, the discretized SIR model implemented in Excel was used, and the infection parameter was obtained by minimizing the squared error function from the real data and the simulated data using the Solver tool. Three approaches were used to obtain the infection parameter: 36-day intervals with the addition of the previous intervals; 36-day intervals without adding the previous intervals; 7-day intervals without adding the previous intervals. The research findings show that in the dynamics of infection caused by Covid-19 through the SIR model, the population can be divided into three compartments: susceptible, infected and removed; where the objective is to identify the number of individuals that move from one compartment to another per unit of time. The adoption of different intervals in the square error minimization process proved to be very relevant for understanding the dynamics and favored different projections of peak and maximum infection values based on consolidated data up to the end of January. At the end of the study, a didactic proposal is made to be worked on with the students of the third year of high school based on mathematical modeling. The problem is initially generated by the teacher and the other steps will be conducted by the students.

MEMBROS DA BANCA:
Presidente - 80963002 - RODRIGO BRUNO ZANIN
Interno - 105502004 - ERICO FERNANDO DE OLIVEIRA MARTINS
Externo à Instituição - LUCIANO ENDLER - IFMT