## Articulo

• Similares en SciELO

## versión impresa ISSN 1409-2433

### Rev. Mat vol.30 no.1 San José ene./jun. 2023

#### http://dx.doi.org/10.15517/rmta.v30i1.50566

Artículo

Mathematical models and simulations of different scenarios of COVID-19 in Brazil

Modelos matemáticos y simulaciones de diferentes escenarios de COVID-19 en Brasil

1IMECC- UNICAMP, Department of Applied Mathematics, Campinas, Brazil; marina@ime.unicamp.br

2 Federal Institute of Parana, IFPR, Pinhais, Brazil; anny.silva@ifpr.edu.br

3 IMECC- UNICAMP, Department of Applied Mathematics, Campinas, Brazil; jmeyer@unicamp.br

Abstract

In this paper, we develop successive mathematical models for describing the first and second waves of COVID-19 in Brazil, including the original strain, the two variants with the highest circulation (Gamma and Delta variants) and population vaccination. We started with a a simple initial model and using mathematical modelling techniques and the Heaviside step function, we improved it according to the necessities of describing the disease’s behaviour, both considering the new variants or vaccination. In all cases, we performed computer simulations and compared the obtained curve with real data from the active cases, which reinforced the model’s efficiency in describing the behaviour of the pandemic and highlighted the importance of population vaccination in describing the dynamics of the infections and reducing cases.

Keywords: COVID-19; mathematical modelling; SARS-CoV-2 variants; mathematical epidemiology; nonlinear systems of ODEs.

Resumen

En este artículo, desarrollamos modelos matemáticos sucesivos para describir la primera y la segunda ola de COVID-19 en Brasil, incluida la cepa original, las dos variantes de mayor circulación (variantes Gamma y Delta) y la vacunación de la población. Partimos de un modelo inicial simple y utilizando técnicas de modelado matemático y la función escalón de Heaviside, lo mejoramos según las necesidades de describir el comportamiento de la enfermedad, tanto considerando las nuevas variantes como la vacunación. En todos los casos, realizamos simulaciones informáticas y comparamos la curva obtenida con datos reales de los casos activos, lo que reforzó la eficiencia del modelo para describir el comportamiento de la pandemia y destacó la importancia de la vacunación de la población para describir la dinámica de los contagios y reducir los casos.

Palabras clave: COVID-19; modelación matemática; variantes de SARS-CoV-2; epidemiologia matemática; sistemas no lineales de EDO.

Mathematics Subject Classification: 92C60

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Acknowledgements

The authors would like to thank to IMECC - Unicamp for support in the development of this work.

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Received: April 01, 2022; Revised: November 15, 2022; Accepted: October 18, 2022