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Mathematics Subject Classification: 62F10; 60G55.
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Revista de Matemática Teoría y Aplicaciones
versión impresa ISSN 1409-2433
Rev. Mat vol.30 no.1 San José ene./jun. 2023
http://dx.doi.org/10.15517/rmta.v30i1.50927
Artículo
A Gompertz mixture approach for modeling the evolution of the COVID-19 dynamics
Mezcla de Gompertz para modelar la evolución de la dinámica del COVID-19
1University of Guanajuato, Department of Mathematics, Guanajuato, México; roberto.vasquez@cimat.mx
2CIMAT, Probability and Statistics, Research Center in Mathematics, Guanajuato, México; farias@cimat.mx
3CIMAT, Probability and Statistics, Research Center in Mathematics, Monterrey and National Council on Science and Technology (CONACYT), Monterrey, México; ulises@cimat.mx
4CIMAT, Probability and Statistics, Research Center in Mathematics, Guanajuato, México; rramosq@cimat.mx
Different countries used the growth Gompertz function at the beginning of the COVID-19 pandemic to model the number of cumulative infected cases since it provides reasonable results. Such a model allows only one mode, but the pandemic evolution has exhibited a multimodal behavior due to the different waves and variants of the COVID-19 virus. Thus, Gompertz’s classical growth model is not well suited to describe a long pandemic with different virus variants. This work presents generalizations of the Gompertz model that can reproduce a multimodal behavior to model the dynamics of infected cases. The models are applied to COVID-19 data from Nuevo Leon, Mexico.
Keywords: COVID-19; Gompertz mixture; Poisson process; Cox process.
Diferentes países usaron la función de crecimiento Gompertz al principio de la pandemia por COVID-19 para modelar el numero acumulado de infectados dado que proporcionaba un ajuste razonable. Este modelo permite una única moda, pero la pandemia evoluciono exhibiendo un comportamiento multimodal debido a las diferentes olas y variantes del COVID-19. Por tanto, el modelo Gompertz clásico de crecimiento no ajusta bien para describir una pandemia larga con diferentes variantes del virus. Este trabajo presenta generalizaciones del modelo Gompertz donde se pueda capturar un comportamiento multimodal para modelar la dinámica de los casos infectados. Este modelo es aplicado a datos de COVID-19 de Nuevo León, México.
Palabras clave: COVID-19; Mezcla de Gompertz; Proceso de Poisson; Proceso de Cox.
Acknowledgements
The author R. Vasquez Martinez is grateful to Ivan Rodriguez Gonzalez (CIMAT) for the multiple discussions and data sharing. In addition, the four authors are very thankful to Dr. Javier Trejos for the invitation to submit this article.
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Received: May 11, 2022; Revised: September 14, 2022; Accepted: October 18, 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
