Mathematical modeling with the SIR model applied to epidemiology: a bibliographic study

Authors

DOI:

https://doi.org/10.14393/BEJOM-v6-2025-77209

Keywords:

Epidemiology, spread of disease, SIR model

Abstract

The present research aimed to carry out a bibliographic study of applying the SIR model in some studies of epidemic or pandemic situations for some States in Brazil. The methodology was to review some works that address applications of differential equations using SIR from which three works were chosen for analysis: the first dealing with hepatitis A in the municipality of Juruti in Pará, the second dealing with dengue fever in Mossoró in Rio Grande do Norte; and the third dealing with the spread of COVID 19 in the State of Maranhao. The research results indicated that the use of modeling tools, such as the SIR model, can be fundamental in helping to understand how contagious diseases spread, this allows public authorities to make the most appropriate decisions to mitigate the disease and the collateral problems that it causes to the population.

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Author Biographies

  • Marcio Costa Araújo Filho, Universidade Federal de Rondônia

    Born in Ouro Preto do Oeste - RO, basic education course in the public network of the State of Rondônia. You have completed your Bachelor's degree in Mathematics from the Federal University of Acre in January 2012. You have completed your Bachelor's degree in Mathematics through the MINTER - UFAM/UFAC program and completed your degree in June 2014. You have completed your Bachelor's degree in Mathematics. PhD in the area of Mathematics for UnB concluded in November 2021 under the guidance of Professor Changyu Xia and guidance of Professor José Nazareno. In January 2013 he entered the federal service as a professor of Basic Technical and Technological Education at the Federal Institute of Acre. In June 2013, he joined the Higher Education Program as assistant professor at the Federal University of Acre - UFAC. Since December 2014 he has been a professor at the Fundação Universidade Federal de Rondônia, UNIR.

  • Reginaldo Tudeia dos Santos, Universidade Federal de Rondônia

    PhD in Climate Sciences in the line of Dynamic/Stochastic Modeling in time and climate (Federal University of Rio Grande do Norte), Master in Mathematical Modeling (Universidade Regional do Noroeste do Estado do Rio Grande do Sul), specialization in Mathematical Education (Federal University of Rondônia), Bachelor's degree in Mathematics (Federal University of Rondônia) and graduation in Sciences (Integrated Faculties of Ariquemes). He is currently a full professor at the Federal University of Rondônia, Ji-Paraná campus. He works mainly in applied mathematics.

  • Letícia Alencar Mendes Martinho, Universidade Federal de Rondônia

    Graduated in Mathematics from the Federal University of Rondônia, completed in 2024.

References

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Alves, R. G. e Oliveira, M. R. A. “Modelagem matem´atica de sistemas epidemiol´ogicos: um modelo SEIR para o sarampo”. Em: Revista de Matem´atica da UFOP 2 (2021), pp. 70–100. URL: https://periodicos.ufop.br/rmat/article/view/ 5148.

Boyce, W. E., Diprima, R. C. e Meade, D. B. Equac¸˜oes diferenciais elementares e problemas de valores de contorno. 11ª ed. Rio de Janeiro: LTC, 2020, p. 425.

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Published

2025-11-28

How to Cite

COSTA ARAÚJO FILHO, Marcio; TUDEIA DOS SANTOS, Reginaldo; ALENCAR MENDES MARTINHO, Letícia. Mathematical modeling with the SIR model applied to epidemiology: a bibliographic study. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, Minas Gerais, v. 6, p. 1–18, 2025. DOI: 10.14393/BEJOM-v6-2025-77209. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/77209. Acesso em: 8 feb. 2026.

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