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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.46 no.1 Bogotá Jan./June 2012

 

Un modelo matemático sobre la dinámica del Mycobacterium tuberculosis en el granuloma

A Mathematical Model on Mycobacterium tuberculosis Dynamics into the Granuloma

EDUARDO IBARGÜEN-MONDRAGÓN1, LOURDES ESTEVA2

1Universidad de Nariño, Pasto, Colombia. Email: edbargun@udenar.edu.co
2Universidad Nacional Autónoma de México, México D. F, México. Email: lesteva@lya.fciencias.unam.mx


Resumen

El propósito de este estudio es evaluar el impacto de la respuesta de las células T y los macrófagos en el control de Mtb dentro del granuloma. Con este fin, proponemos un sistema de ecuaciones diferenciales ordinarias para modelar la interacción entre macrófagos no infectados, macrófagos infectados, células T y bacilos de Mtb en el granuloma.

Palabras clave: Ecuaciones diferenciales ordinarias, soluciones deequilibrio, tuberculosis, inmunología.


2000 Mathematics Subject Classification: 37C75, 92B05.

Abstract

The purpose of this study is to evaluate the impact of the response of T cells and macrophages in the control of Mtb into the granuloma. To this end, we propose a system of ordinary differential equations to model the interaction among uninfected macrophages, infected macrophages, T cells and Mtb bacilli into the granuloma.

Key words: Ordinary Differential Equations, Equilibrium Solutions, Tuberculosis, Immunology.


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Referencias

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[4] F. Gantmacher, The Theory of Matrices, Chelsea House Publishers, London, United Kingdom,         [ Links ] 1960.

[5] E. Ibargüen-Mondragón, L. Esteva, and L. Chávez-Galán, 'A Mathematical Model for Cellular Immunology of Tuberculosis', J. Mathematical Biosciences and Engineering 8, 4 (2011), 973-986.         [ Links ]

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[7] G. Magombedze, W. Garira, and E. Mwenje, 'Modelling the Human Immune Response Mechanisms to Mycobacterium Tuberculosis Infection in the Lungs', J. Mathematical Biosciences and engineering 3, 4 (2006), 661-682.         [ Links ]

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[9] Palomino, Leáo, and Ritacco, Tuberculosis 2007, From Basic Science to Patient Care, Tuberculosistextbook.com, Brasil,         [ Links ] 2007.

[10] D. Russell, 'Who Puts the Tubercle in Tuberculosis?', Nature Rev Microbilogy jan, 5 (2007), 39-47.         [ Links ]

[11] M. Tsai, S. Chakravarty, G. Zhu, J. Xu, K. Tanaka, C. Koch, J. Tufariello, J. Flynn, and J. Chan, 'Characterization of the Tuberculous Granuloma in Murine and Human Lungs: Cellular Composition and Relative Tissue Oxygen Tension', Cell Microbiol 8, 2 (2006), 218-232.         [ Links ]

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(Recibido en octubre de 2011. Aceptado en marzo de 2012)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv46n1a04,
AUTHOR = {Ibargüen-Mondragón, Eduardo and Esteva, Lourdes},
TITLE = {{Un modelo matemático sobre la dinámica del \emph{Mycobacterium tuberculosis} en el granuloma}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2012},
volume = {46},
number = {1},
pages = {39--65}
}

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