A SIR model and the Routh-Hurwitz test

Authors

  • Natanael de Jesus Oliveira State University of Rio de Janeiro
  • Patrícia Nunes da Silva State University of Rio de Janeiro

Keywords:

Epidemiology. Compartmental models. Equilibrium points. Routh-Hurwitz test.

Abstract

Compartmental models are used in epidemiology to describe the dynamics of disease transmission. The objective of this study is to analyze the stability of equilibrium points in a compartmental model where birth and death rates are not necessarily equal, and birth rate depends on the total population size. To analyze the stability of equilibrium points, we applied the so-called Routh-Hurwitz test. For completeness, we also provide a proof of the Routh-Hurwitz test. Through the application of the test, we conclude that the equilibrium points, both disease-free and endemic, in the studied compartmental model are asymptotically stable.

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Author Biographies

Natanael de Jesus Oliveira, State University of Rio de Janeiro

Completed high school at CIEP MARIO QUINTANA (2011). Currently, he is studying for a bachelor's degree in Mathematics at the State University of Rio de Janeiro.

Patrícia Nunes da Silva, State University of Rio de Janeiro

She has a Bachelor's degree in Mathematics (1996), a Master's degree in Applied Mathematics (1999) and a PhD in Applied Mathematics from the State University of Campinas (2003). She is currently an Associate Professor at the State University of Rio de Janeiro, member of the editorial board of Cadernos do IME. Série Matemática, reviewer for several periodicals. He works in the postgraduate and Computational Sciences programs and in the master's program in mathematics on a national network (PROFMAT) at the Institute of Mathematics and Statistics at UERJ. She has experience in the area of ​​Mathematics and Mathematics Teaching.

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Published

2024-09-24

How to Cite

de Jesus Oliveira, N., & Nunes da Silva, P. (2024). A SIR model and the Routh-Hurwitz test. Revista Brasileira De Iniciação Científica, 024041. Retrieved from https://periodicoscientificos.itp.ifsp.edu.br/index.php/rbic/article/view/1436

Issue

Volume 11, 2024 – publicação Contínua

Section

Artigos

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Copyright (c) 2024 Revista Brasileira de Iniciação Científica

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