Um Modelo Matemático Discreto do tipo SIR aplicado à dados de casos da COVID-19 no Estado de Mato Grosso
DOI:
https://doi.org/10.22481/intermaths.v3i1.10279Keywords:
Modelagem Matemática, Simulações Numéricas, Modelo Matemático Discreto, Método dos Mínimos QuadradosAbstract
In this paper we present a discrete mathematical model of the SIR type in which data related to the number of cases in the State of Mato Grosso, Brazil are used to create simulations and predictions about the phenomenon of disease propagation. The model parameters were estimated using data from the scientific literature and also using the Minimum Squares Method. Among the simulations present in this work, those that estimate the impact of adherence, or not, of the population to social distancing measures and the use of masks, stand out. One of the results shows that if 70% of the population adhered to both measures, we would have the extinction of the contagion in a few months. This research had an exploratory character and its results are only indicative and do not have a conclusive character.
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[1] SES, Secretaria de Estado de Saúde de Mato Grosso, “Painel Informativo COVID-19,” 2021. http://www.saude.mt.gov.br/painelcovidmt2/ Acesso em: 09/05/2021.
[2] W. Kermack, A. McKendrick, “A contribution to the mathematical theory of epidemics,” in Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, vol. 115, no. 772, pp. 700-721, 1927.
[3] O. Diekmann, J. A. P. Heesterbeek. Mathematical Epidemiology of infectious diseases: model building, analysis and interpretatiton, England, John Wiley and Sons Ltda, 2000.
[4] Z. Ma, “Some Recent Results on Epidemic Dynamics Obtained by Our Group,” in Modeling and Dynamics of Infectious Diseases, Z. Ma, Y. Zhou and J. Wu, Eds. Series in Contemporary Applied Mathematics, Vol. 11. Beijing and World Scientific; Singapore: Higher Ed. Press, 2009; pp. 1–35.https://doi.org/10.1142/9789814261265_0001
[5] T. Sitthiwirattham, A. Zeb, S. Chasreechai, Z. Eskandari, M. Tilioula and S. Djilali, “Analysis of a discrete mathematical COVID-19 model,” Results in Physics, vol. 28, p. 104668, 2021. https://doi.org/10.1016/j.rinp.2021.104668
[6] L. M. E. Assis, A. Mendonça and R. A. Assis, “Ajuste de curvas utilizando dados do coronavírus COVID-19 e sistemas dinâmicos discretos,” Biomatemática, vol. 30, pp. 93-110, 2020.
[7] P. R. Zingano. et al. Observações sobre previsões da evolução da COVID-19 por modelos matemáticos. Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, 2020. https://www.ufrgs.br/ime/wp-content/uploads/2020/04/Evolu%C3%A7%C3%A3o_da_Covid1-1.pdf
[8] T. A. Mellan, H. H Hoeltgebaum, S. Mishra, C. Whittaker, R. P Schnekenberg, A. Gandy, H. J. T.Unwin, M. A. C. Vollmer, H. Coupland, I. Hawryluk, N. R. Faria, J. Vesga, H. Zhu, M. Hutchinson, O. Ratmann, M. Monod, K. Ainslie, M. Baguelin, S. Bhatia, A. Boonyasiri, N. Brazeau, G. Charles, L.V. Cooper, Z. Cucunuba, G. Cuomo-Dannenburg, A. Dighe, B. Djaafara, J. Eaton, S. L. van Elsland, R. FitzJohn, K. Fraser, K. Gaythorpe, W. Green, S. Hayes, N. Imai, B. Jeffrey, E. Knock, D. Laydon, J. Lees, T. Mangal, A. Mousa, G. Nedjati-Gilani, P. Nouvellet, D. Olivera, K. V. Parag, M. Pickles, H. A. Thompson, R. Verity, C. Walters, H. Wang, Y. Wang, O. J. Watson, L. Whittles, X. Xi, L. Okell, I. Dorigatti, P. Walker, A. Ghani, S. Riley, N. M Ferguson, C. A. Donnelly, S. Flaxman and S. Bhatt, Estimating COVID-19 cases and reproduction number in Brazil, Report 21, Imperial College London, May/2020. :https://doi.org/10.25561/78872
[9] A. El Bhih, Y. Benfatah, A. Kouidere and M. Rachik, “A discrete mathematical modeling of transmission of COVID-19 pandemic using optimal control,” Communications in Mathematical Biology and Neuroscience, 2020, Artigo ID 75. https://doi.org/10.28919/cmbn/4780
[10] G. B. Almeida, “Aplicação de modelos matemáticos em pandemias: um estudo de comportamento epidemiológico a partir da Covid-19,” Tese de doutorado do Programa de Pós-Graduação em Doenças Tropicais, Faculdade de Medicina de Botucatu, Universidade Estadual Paulista Júlio Mesquita Filho, 2022.
[11] CDC, Centers for Disease Control and Prevention, “Interim Guidance on Ending Isolation and Precautions for Adults with COVID-19,” 2021. https://www.cdc.gov/coronavirus/2019-ncov/hcp/duration-isolation.html#print Acesso em: 24/04/2021.
[12] S.F. Lumley, D. O’Donnell, N.E. Stoesser, P.C. Matthews, A. Howarth, S.B. Hatch, B.D. Marsden, S. Cox, T. James, F. Warren, L.J. Peck, T.G. Ritter, Z. de Toledo, L. Warren, D. Axten, R.J. Cornall, E.Y. Jones, D.I. Stuart, G. Screaton, D. Ebner, S. Hoosdally, M. Chand, D.W. Crook, A.-M. O’Donnell, C.P. Conlon, K.B. Pouwels, A.S. Walker, T.E.A. Peto, S. Hopkins, T.M. Walker, K. Jeffery, and D.W. Eyre, “Antibody status and incidence of SARS-CoV-2 infection in health care workers,” New England Journal of Medicine, vol. 384, no. 6, pp. 533-540, 2021. http://dx.doi.org/10.1056/NEJMoa2034545
[13] D. Cromer, J. A. Juno, D. Khoury, A. Reynaldi, A. K. Wheatley, S. J. Kent and M. P. Davenport, “Prospects for durable immune control of SARS-CoV-2 and prevention of reinfection,” vol. 21, no. 6, pp. 395-404, 2021. https://doi.org/10.1038/s41577-021-00550-x
[14] A. L. Nogueira, C. L. Nogueira, A. W. Zibetti, N. Roqueiro, O. Bruna-Romero and B. A. M. Carciofi, “Estimativa da subnotificação de casos da covid-19 no estado de Santa Catarina,” Notícias UFSC, Florianópolis, 2020. Disponível em: https://noticias.paginas.ufsc.br/files/2020/05/aqui.pdf
[15] IBGE, Instituto Brasileiro de Geografia e Estatística , “Cidades Panorama,” 2021. https://cidades.ibge. gov.br/brasil/mt/panorama Acesso em: 03/01/2021.
[16] M. B. Prado, B. B. P. Antunes, L. S. L. Bastos, I. T. Peres, A. A. B. da Silva, L. F. Dantas, F. A. Baião, P. Maçaira, S. Hamacher and F. A. Bozza, “Análise da subnotificação de COVID-19 no Brasil,” Revista Brasileira de Terapia Intensiva (online), 2020. https://doi.org/10.5935/0103-507X.20200030
[17] J. A. Azevedo, “Um modelo matemático discreto do tipo SIR aplicado à COVID-19 e considerações sobre o uso da Modelagem Matemática no Ensino Médio,” Dissertação de Mestrado do Programa de Pós-Graduação Profissional em Matemática - PROFMAT, Matemática, Universidade Estadual de Mato Grosso, 2021.
[18] P. A. Morettin, W. O. Bussab. Estatística básica, Saraiva Educação SA, São Paulo, 2004.
[19] J.-M. Wendling, T. Fabacher, P.-P. Pébaÿ, I. Cosperec, and M. Rochoy, “Experimental efficacy of the face shield and the mask against emitted and potentially received particles,” International Journal of Environmental Research and Public Health, vol. 18, no. 4, p. 1942, 2021. https://doi.org/10.3390/ijerph18041942
[20] M. R. Gonçalves, R. C. P. dos Reis, R. P. Tólio, L. C. Pellanda, M. I. Schmidt, N. Katz, S. S. Mengue, P. C. Hallal, B. Lessa Horta, M. F. Silveira, R. N. Umpierre, C. G. Bastos-Molina, R. S. da Silva and B. B. Duncan, “Social Distancing, Mask Use and the Transmission of SARS-CoV-2: A Population-Based Case-Control Study,” SSRN - Preprints with Lancet, 2020. https://dx.doi.org/10.2139/ssrn.3731445
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