Discrete models for analyzing the behavior of COVID-19 pandemic in the State of Mexico, Mexico

Erik A. Vázquez Jiménez; Jesús Martínez Martínez; Leonardo D. Herrera Zuniga; J. Guadalupe Reyes Victoria; Erik A. Vázquez Jiménez; Jesús Martínez Martínez; Leonardo D. Herrera Zuniga; J. Guadalupe Reyes Victoria

doi:10.3934/mbe.2023014

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 296-317. doi: 10.3934/mbe.2023014

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Discrete models for analyzing the behavior of COVID-19 pandemic in the State of Mexico, Mexico

1.
Tecnologico de Estudios Superiores de Huixquilucan-TESH, Estado de Mexico, Mexico
2.
Universidad Autonoma del Estado de Morelos, Estado de Morelos, Mexico
3.
Universidad Autonoma Metropolitana, Unidad Iztapalapa, CP 09340, Cd. de Mexico, Mexico

Academic Editor: Pierre Magal

Received: 07 July 2022 Revised: 07 September 2022 Accepted: 08 September 2022 Published: 08 October 2022

In this paper we analyze the behavior of the COVID-19 pandemic during a certain period of the year 2020 in the state of Mexico, Mexico. For this, we will use the discrete models obtained by the first, third and fourth authors of this work. The first is a one-dimensional model, and the second is two-dimensional, both non-linear. It is assumed that the population of the state of Mexico is constant and that the parameters used are the infection capacity, which we will initially assume to be constant, and the recovery and mortality parameters in that state. We will show that even when the statistical data obtained are disperse, and the process could be stabilized, this has been slow due to chaotic mitigation, creating situations of economic, social, health and political deterioration in that region of the country. We note that the observed results of the behavior of the epidemic during that period for the first variants of the virus have continued to be observed for the later variants, which has not allowed the eradication of the pandemic.
- pandemic,
- two dimensional discrete dynamics,
- attractor-repulser fixed points,
- mitigation,
- Chaos,
- eradication
Citation: Erik A. Vázquez Jiménez, Jesús Martínez Martínez, Leonardo D. Herrera Zuniga, J. Guadalupe Reyes Victoria. Discrete models for analyzing the behavior of COVID-19 pandemic in the State of Mexico, Mexico[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 296-317. doi: 10.3934/mbe.2023014

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Abstract

In this paper we analyze the behavior of the COVID-19 pandemic during a certain period of the year 2020 in the state of Mexico, Mexico. For this, we will use the discrete models obtained by the first, third and fourth authors of this work. The first is a one-dimensional model, and the second is two-dimensional, both non-linear. It is assumed that the population of the state of Mexico is constant and that the parameters used are the infection capacity, which we will initially assume to be constant, and the recovery and mortality parameters in that state. We will show that even when the statistical data obtained are disperse, and the process could be stabilized, this has been slow due to chaotic mitigation, creating situations of economic, social, health and political deterioration in that region of the country. We note that the observed results of the behavior of the epidemic during that period for the first variants of the virus have continued to be observed for the later variants, which has not allowed the eradication of the pandemic.

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