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Mathematical Medicine and Biology Advance Access originally published online on October 23, 2006
Mathematical Medicine and Biology 2007 24(1):35-56; doi:10.1093/imammb/dql026
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Within-host population dynamics of antibiotic-resistant M. tuberculosis

Justino Alavez-Ramírez1, J. Rogelio Avendano Castellanos2, Lourdes Esteva**,3, José Antonio Flores3, José Luis Fuentes-Allen4, Gisela García-Ramos5, Guillermo Gómez6 and Jesús López-Estrada6

1 División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Cunduacán 86690, Tabasco, México, 2 Departamento de Farmacología, Facultad de Medicina, Universidad Nacional Autónoma de México, 04510 México, DF, 3 Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México, DF, 4 Hospital de Infectología, Centro Médico la Raza, Instituto Mexicano del Seguro Social, México, DF, 5 Department of Biology, University of Kentucky, 101 Morgan Building, Lexington, KY 40506, USA, 6 Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México, DF

** Email: lesteva{at}servidor.unam.mx


  Abstract

Mathematical models for the population dynamics of de novo resistant Mycobacterium tuberculosis within individuals are studied. The models address the use of one or two antimicrobial drugs for treating latent tuberculosis (TB). They consider the effect of varying individual immune response strength on the dynamics for the appearance of resistant bacteria. From the analysis of the models, equilibria and local stabilities are determined. For assessing temporal dynamics and global stability for sensitive and drug-resistant bacteria, numerical simulations are used. Results indicate that for a low bacteria load that is characteristic of latent TB and for small reduction in an immune response, the use of a single drug is capable of curing the infection before the appearance of drug resistance. However, for severe immune deficiency, the use of two drugs will provide a larger time period before the emergence of resistance. Therefore, in this case, two-drugs treatment will be more efficient in controlling the infection.

Keywords: tuberculosis; antimicrobial resistance; mathematical model; isoniazid; rifampin

Received on 28 February 2006. Revised on 12 September 2006.


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