Mathematical Biosciences and Engineering, 2011, 8(4): 973-986. doi: 10.3934/mbe.2011.8.973.

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A mathematical model for cellular immunology of tuberculosis

1. Departamento de Matemáticas y Estadística,, Universidad de Nariño, Pasto, Clle 18 - Cra 50, Colombia, Posgrado en Ciencias Matemáticas, UNAM, 04510 DF
2. Departamento de Matemáticas, Facultad de Ciencias,, Universidad Nacional Autónoma de M ́exico, 04510, DF
3. Departamento de Bioquímica, Instituto Nacional de Enfermedades Respiratorias ”Ismael Cosio Villegas”, Calzada Tlalpan 4502, Colonia sección XVI, 14080 DF

Tuberculosis (TB) is a global emergency. The World Health Organization reports about 9.2 million new infections each year, with an average of 1.7 million people killed by the disease. The causative agent is Mycobacterium tuberculosis (Mtb), whose main target are the macrophages, important immune system cells. Macrophages and T cell populations are the main responsible for fighting the pathogen. A better understanding of the interaction between Mtb, macrophages and T cells will contribute to the design of strategies to control TB. The purpose of this study is to evaluate the impact of the response of T cells and macrophages in the control of Mtb. To this end, we propose a system of ordinary differential equations to model the interaction among non-infected macrophages, infected macrophages, T cells and Mtb bacilli. Model analysis reveals the existence of two equilibrium states, infection-free equilibrium and the endemically infected equilibrium which can represent a state of latent or active infection, depending on the amount of bacteria.
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Keywords qualitative analysis; immunology.; numerical solu- tions; tuberculosis; Ordinary differential equations

Citation: Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences and Engineering, 2011, 8(4): 973-986. doi: 10.3934/mbe.2011.8.973

 

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