English (pdf)
Article in xml format
Article references
Automatic translation
Send this article by e-mail
Permalink
Mathematics Subject Classification: 92C60
Ver contenido completo en PDF.
Services on Demand
Journal
Article
Indicators
-
Cited by SciELO -
Access statistics
Related links
-
Similars in
SciELO
Share
Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.30 n.1 San José Jan./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
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.
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.
Acknowledgements
The authors would like to thank to IMECC - Unicamp for support in the development of this work.
References
J, J, V, Bavel; K, Baicker; P, S, Boggio; V, Capraro; A, Cichocka; M, Cikara. Using social and behavioural science to support COVID-19 pandemic response, Nature Human Behaviour 4(2020), no.5, 460-471. Doi: 10.1038/s41562-020-0884-z. [ Links ]
Centers for Disease Control and Prevention, COVID-19: SARS-CoV-2 variant classifications and definitions, 2021. Available at https://www.cdc.gov/coronavirus/2019-ncov/variants/variant-classifications.html, consulted on 23-Nov-2021. [ Links ]
R, S, Diaz; T, Vergara. The COVID-19 second wave: A perspective to be explored, The Brazilian Journal of Infectious Diseases 25(2021), no.1, 275- 277. Doi: 10.1016/j.bjid.2020.101537. [ Links ]
Drug, Discovery and Development. U.S. government classifies threat levels of SARS-CoV-2 variants, 2021. Available at https://www.drugdiscoverytrends.com/u-s-government-classifies-threat-levels-of-sars-cov-2-variants/, consulted on 30-Nov-2021. [ Links ]
European Centre for Disease Prevention and Control, Threat assessment brief: emergence of SARS-CoV-2 B.1.617 variants in India and situation in the EU/EEA, 2021. Available at https://www.ecdc.europa.eu/en/publications-data/threat-assessment-emergence-sars-cov-2-b1617-variants, consulted on 10-Nov-2021. [ Links ]
D, W, Eyre; D, Taylor; M, Purver; D, Chapman; T, Fowler; K, B, Pouwels et al. The impact of SARS-CoV-2 vaccination on Alpha & Delta variant transmission, medRxiv, 2021. Doi: 10.1101/2021.09.28.21264260. [ Links ]
C, Huang; Y, Wang; X, Li; L, Ren; J, Zhao; Y, Hu et al. Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, Lancet 395(2020), no.10223, 497-506. Doi: 10.1016/S0140-6736(20)30183-5 [ Links ]
Instituto Brasileiro de Geografia e Estatística, Projeção da população do Brasil e das Unidades da Federação, 2021. Available at https://www.ibge.gov.br/apps/populacao/projecao/, consulted on 30-Nov-2021. [ Links ]
Inloco, Mapa brasileiro da COVID-19, 2021. Available at https://mapabrasileirodacovid.inloco.com.br/pt/, consulted on 12-Nov-2021. [ Links ]
Instituto Butantan, Autorização temporária de uso emergencial da vacina adsorvida COVID-19 (inativada) - Dizeres de texto de bula, 2021. Available at https://vacinacovid.butantan.gov.br/bulas, consulted on 01-Oct-2021. [ Links ]
J, F, C, A, Meyer; M, Lima; C, Espitia; F, Longo; B, Laiate; A, Gois et al. Different approaches to the modelling of COVID-19, Trends Comput. Appl. Math. 22(2021), no. 4. Doi: 10.5540/tcam.2021.022.04.00515 [ Links ]
Ministério da Saúde, Brasil confirma primeiro caso da doença, 2021. Available at https://www.saude.gov.br/noticias/agencia-sau-de/46435-brasil-confirma-primeiro-caso-de-novo-coronavirus, consulted on 05-Sep-2021. [ Links ]
Ministerio da Saude, Entregas de vacinas Covid-19, 2021. Available at https://www.gov.br/saude/pt-br/coronavirus/entregas-de-vacinas-covid-19, consulted on 30-Nov-2021. [ Links ]
Our World in Data, Brazil: Coronavirus pandemic country profile, 2021. Available at https://ourworldindata.org/coronavirus/country/brazil, consulted on 30-Nov-2021. [ Links ]
Pfizer/BioNTech, Real-world evidence confirms high effectiveness of Pfizer-BioNTech COVID-19 vaccine and profound public health impact of vaccination one year after pandemic declared, 2021. Available at https://www.pfizer.com/news/press-release/press-release-detail/real-world-evidence-confirms-high-effectiveness-pfizer, consulted on 12-Nov-2021. [ Links ]
W, M, Souza; M, R, Amorim; R, Sesti-Costa; L, D, Coimbra; N, S, Brunetti; DA, Toledo-Teixeira et al. Neutralisation of SARS-CoV-2 lineage P.1 by antibodies elicited through natural SARS-CoV-2 infection or vaccination with an inactivated SARS-CoV-2 vaccine: an immunological study, Lancet Microbe 2(2021), e527-35. Doi: 10.1016/S2666-5247(21)00129-4 [ Links ]
UNICEF, What you need to know about the Delta variant. Learn how to keep yourself and your family safe from the Delta variant of COVID-19, 2021. Available at https://www.unicef.org/coronavirus/what-you-need-know-about-delta-variant, consulted on 02-Nov-2021. [ Links ]
M, Voysey; S, A, C, Clemens; S, A, Madhi; L, Y, Weckx; P, M, Folegatti; P, K, Aley. Single-dose administration and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine: a pooled analysis of four randomised trials, Lancet 397(2021), 881-91. Doi: 10.1016/S0140-6736(21)00432-3 [ Links ]
World Health Organization (2021). Background document on the Janssen Ad26.COV2.S (COVID-19) vaccine, 2021. Available at https://apps.who.int/iris/handle/10665/340180, consulted on 02-Nov-2021. [ Links ]
Worldometers, COVID-19 Coronavirus Pandemic, 2021. Available at https://www.worldometers.info/coronavirus/, consulted on 30-Nov-2021. [ Links ]
Received: April 01, 2022; Revised: November 15, 2022; Accepted: October 18, 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
