Stability analysis in COVID-19 within-host model with immune response

Almocera, Alexis Erich S.; Quiroz, G.; Hernandez‐Vargas, Esteban A.

doi:10.1016/j.cnsns.2020.105584

Cited by 53 publications

(42 citation statements)

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“…A large number of works use mathematical and computational tools to model the Human Immune System (HIS) using distinct techniques, such as ordinary differential equations (ODEs) ( Perelson, 1989 ; Baker et al, 1997 ; Chang et al, 2005 ; Vodovotz et al, 2006 ; Jarrett et al, 2015 ; Bonin et al, 2016 ), partial differential equations (PDEs) ( Pettet et al, 1996 ; Su et al, 2009 ; Flegg et al, 2012 ; Pigozzo et al, 2013 ; Quintela et al, 2014 ), stochastic methods ( Chao et al, 2004 ; Xavier et al, 2017 ), cellular automaton and agents ( Celada and Seiden, 1992 ; Morpurgo et al, 1995 ; Kohler et al, 2000 ; Bernaschi and Castiglione, 2001 ; Pappalardo et al, 2018 ). On the other hand, very few papers were published describing the dynamics of SARS-CoV-2 ( Almocera et al, 2020 ; Du and Yuan, 2020 ; Hernandez-Vargas and Velasco-Hernandez, 2020 ; Xavier et al, 2020 ), although some additional non-peer-reviewed papers can also be found on the internet. Three out four published works ( Almocera et al, 2020 ; Du and Yuan, 2020 ; Hernandez-Vargas and Velasco-Hernandez, 2020 ) are based on the target cell-limited model proposed by Perelson (2002) : a system of three ODEs to model target cells, infected cells, and viruses.…”

Section: Related Workmentioning

confidence: 99%

“…On the other hand, very few papers were published describing the dynamics of SARS-CoV-2 ( Almocera et al, 2020 ; Du and Yuan, 2020 ; Hernandez-Vargas and Velasco-Hernandez, 2020 ; Xavier et al, 2020 ), although some additional non-peer-reviewed papers can also be found on the internet. Three out four published works ( Almocera et al, 2020 ; Du and Yuan, 2020 ; Hernandez-Vargas and Velasco-Hernandez, 2020 ) are based on the target cell-limited model proposed by Perelson (2002) : a system of three ODEs to model target cells, infected cells, and viruses. In this work, we use a set of fifteen ODEs to model not only the virus but also immune cells, antibodies and cytokines.…”

Section: Related Workmentioning

confidence: 99%

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A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19

Reis

Pigozzo

Bonin³

et al. 2021

Front. Mol. Biosci.

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By June 2021, a new contagious disease, the Coronavirus disease 2019 (COVID-19), has infected more than 172 million people worldwide, causing more than 3.7 million deaths. Many aspects related to the interactions of the disease’s causative agent, SAR2-CoV-2, and the immune response are not well understood: the multiscale interactions among the various components of the human immune system and the pathogen are very complex. Mathematical and computational tools can help researchers to answer these open questions about the disease. In this work, we present a system of fifteen ordinary differential equations that models the immune response to SARS-CoV-2. The model is used to investigate the hypothesis that the SARS-CoV-2 infects immune cells and, for this reason, induces high-level productions of inflammatory cytokines. Simulation results support this hypothesis and further explain why survivors have lower levels of cytokines levels than non-survivors.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19

Reis

Pigozzo

Bonin³

et al. 2021

Front. Mol. Biosci.

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“…Mathematical models are usually used to depict the propagation of a virus [6][7][8][9][10][11][12], and so many scholars have proposed a lot of mathematical models to study the spreading laws of the COVID-19 virus [13][14][15][16][17]. Although strengthening personal protection helps to resist the virus [18], it is still very important to understand the law of virus transmission.…”

Section: Introductionmentioning

confidence: 99%

A time-delay COVID-19 propagation model considering supply chain transmission and hierarchical quarantine rate

Yang

Zhang

2021

Adv Differ Equ

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In this manuscript, we investigate a novel Susceptible–Exposed–Infected–Quarantined–Recovered (SEIQR) COVID-19 propagation model with two delays, and we also consider supply chain transmission and hierarchical quarantine rate in this model. Firstly, we analyze the existence of an equilibrium, including a virus-free equilibrium and a virus-existence equilibrium. Then local stability and the occurrence of Hopf bifurcation have been researched by thinking of time delay as the bifurcation parameter. Besides, we calculate direction and stability of the Hopf bifurcation. Finally, we carry out some numerical simulations to prove the validity of theoretical results.

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“…En este sentido, entender más sobre la dinámica del SAR-CoV-2, así como mejorar la estimación de los parámetros de la infección viral, será determinante para actuar de mane-ra eficiente. El trabajo desarrollado por Hernández-Vargas y Velasco-Hernández puede servir para la evaluación de enfoques teóricos de control para adaptar nuevos fármacos contra COVID-19 (Hernandez-Vargas and Velasco-Hernandez, 2020;Almocera et al, 2021).…”

Section: A Manera De Introducciónunclassified

Editorial

Villafuerte-Segura

Ávila-Pozos

2021

ICBI

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A casi un año con cinco meses de ver modificado nuestras vidas para salvaguardar la integridad y contener la enfermedad denominado COVID-19, en nuestro país se han concluido con las jornadas de vacunación de la Etapas 1 a la Etapa 3, correspondiente a personal de salud, adultos mayores a 50 años y personal de sector educativo. Esto augura un posible regreso a las aulas en modalidad híbrida y a bloques, perspectiva sugerida y difundida por las autoridades competentes al momento de escribir estas líneas. Aunque se podría ahondar más acerca de las acciones, quehaceres, consecuencias y de más, sobre este tema, en esta ocasión se dejará espacio en la editorial al Dr. Roberto Ávila Pozos que con su escrito titulado “La modelación matemática durante la pandemia” externará con más profundidad y profesionalismo al respecto. Ahora bien y como es costumbre, el equipo editorial de Pädi Boletín Científico de Ciencias Básicas e Ingenierías del ICBI de la Universidad Autónoma del Estado de Hidalgo, extiende un cordial agradecimiento a los autores que con sus contribuciones, cada vez más crecientes y demandantes, han logrado que las ediciones de nuestra revista no se detengan, más aún, nos complace anunciarles que a partir de esta edición, el número de manuscritos publicados asciende a 20. Esto sin duda nos llena de placer y nos incentiva a seguir trabajando para mejorar la calidad y la cantidad de manuscritos publicados. Sin más preámbulo y con base a la recepción de manuscritos para el Vol. 9 No. 17 de Pädi, es grato presentarles la reseña de los 20 manuscritos que conforman esta edición, esperando sea de gran interés para el lector e invitando a consultar el texto completo del manuscrito de su afinidad: 14 manuscritos de compañeros/colegas de diferentes Áreas, Institutos y/o Escuelas Superiores de la UAEH, 2 manuscritos en colaboración entre investigadores de la UAEH y de PEMEX, 1 manuscrito del Instituto Tecnológico de Orizaba, 1 manuscrito en colaboración entre investigadores de la UAEH y Tecnológico de Monterrey, 1 manuscrito en colaboración entre investigadores de la UAEH y la Universidad Autónoma de Ciudad Juárez, así como 1 manuscrito en colaboración entre investigadores de la UAEH y la Universidad Autónoma de Tamaulipas.

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Stability analysis in COVID-19 within-host model with immune response

Abstract: Highlights Mathematical model to represent viral dynamics in COVID-19 patients. Stability Analysis in COVID-19 Within-Host Model Bifurcation analysis suggests that the virus replicates fast to overcome T cells.

Cited by 53 publications

References 32 publications

A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19

A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19

A time-delay COVID-19 propagation model considering supply chain transmission and hierarchical quarantine rate

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