Simple mathematical models on macrophages and CTL responses against Mycobacterium tuberculosis

Eduardo Ibargüen-Mondragón, Lourdes Esteva

Resumen


Resumen

En este trabajo se formulan cuatro modelos matemáticos que intentan describir aspectos básicos de la dinámica de la infección con el Micobacterium tuberculosis (Mtb) en diferentes etapas.
El propósito de este estudio es evaluar el impacto de la respuesta de las células T y los macrófagos en el control del Mtb.

 

Abstract

In this work we formulate fourth mathematical models trying to describe basic aspects
into the dynamics of theMycobacterium tuberculosis (Mtb) infection at different stages. The purpose
of this study is to evaluate the impact of the response of T cells and macrophages in the control of
Mtb.


Palabras clave


Modelo matemático, Tuberculosis, Estabilidad, Inmunología, soluciones de equilibrio, Mathematical model, Tuberculosis, Stability, Immunology, Equilibrium solutions.

Texto completo:

ARCHIVO PDF (English)

Referencias


Global tuberculosis control: surveillance, planning, financing: WHO report 2008.

WHO/HTM/TB/2008.393. 31

Palomino-Leo-Ritacco, Tuberculosis 2007, From basic science to patient care. TuberculosisTextbook.

com, 2007, first edition. 31

J. Chan,J. Flynn, The immunological aspects of latency in tuberculosis, Clin. Immunol.

;110(1): 2-12. 31, 40

A. M. Gallegos, E. G. Pamer, M. S. Glickman, Delayed protection by ESAT-6-specific

effector CD4+ T cells after airborne M. tuberculosis infection. J. Exp. Med. 2008 Sep

;205(10):2359-68. 31, 40

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 Microbiology, 8 (2006),

–232. 32

R. Antia, J. Koella, V. Perrot, Model of the Whitin-host dynamics of persistent mycobacterial

infections. Proc. R. Soc. Lond. B. 263(1996) 257-263. 32

D. Kirschner, Dynamics of Co-infection with M. tuberculosis and HIV-1. Theor Popul

Biol. 55(1999) 94-109. 32

DE. Kirschner, D. Sud, C. Bigbee, JL. Flynn, Contribution of CD8+T Cells to Control

of Mycobacterium tuberculosis Infection. The Journal of Immunology. 2006 April

;176(7)1: 4296-4314. 32

G. Magombedze, W. Garira, E. Mwenje, Modellingthe human immune response mechanisms

to mycobacteriumtuberculosis infection in the lungs, J.Mathematical Biosciences

and engineering, 2006, 3(3):661-682. 32

G. Magombedze, N. Mulder, Understanding TB latency using computational and dynamic

modelling procedures,Infection, Genetics and Evolution, 2013(13): 267283. 32

E. Ibargüen-Mondragón , L. Esteva, L. Chávez-Galán, A mathematical model for cellular

immunology of tuberculosis. J. Mathematical Eiosciences and Engineering, 2011

(4): 976-986. 32, 40

E. Ibargüen-Mondragón , L. Esteva, L., Un modelo matemático sobre la dinámica del

Mycobacterium tuberculosis en el granuloma. Revista Colombiana de Matemáticas, 2012

(1): 39-65. 32

E. Ibargüen-Mondragón and L. Esteva, L., On CTL Response against Mycobacterium

tuberculosis. Applied Mathematical Sciences, 2014 8(48):2383-2389. 32, 38, 39

J. Romero, E. Ibargüen-Mondragón, L. Esteva, Un modelo matemático sobre bacterias

sensibles y resistentes a antibióticos, Matemáticas: Enseñanza Universitaria, 2011

(1):5573. 32

E. Ibargüen-Mondragón, L. Esteva, On the interactions of sensitive and resistant Mycobacterium

tuberculosis to antibiotics, Math Biosci, 2013(246): 8493. 32

E. Ibargüen-Mondragón, S. Mosquera, M. Cerón, EM. Burbano-Rosero, SP. Hidalgo-

Bonilla, L. Esteva, JP. Romero-Leiton, Mathematical modeling on bacterial resistance

to multiple antibiotics caused by spontaneous mutations, BioSystems, 2014(117): 6067.

JP. Romero-Leiton and E. Ibargüen-Mondragón, Sobre la resistencia bacteriana hacia

antibióticos de acción bactericida y bacteriostática, Rev Integ., 2014(32): 101-116. 32

E. Ibargüen-Mondragón, EM. Burbano-Rosero, L. Esteva, JP. Romero-Leiton, Mathematical

modeling of bacterial resistance to antibiotics by mutations and plasmids,

Journal of Biological Systems, 2016 24(1): 1-18. 32

E. Ibargüen-Mondragón, L. Esteva, L. Chávez-Gálan, Estabilidad global para un modelo

matematico sobre la respuesta inmune innata de macrofagos contra elMicobacterium

tuberculosis, Revista Sigma, 2010 10(1): 1-17. 32

J. Alavez, J. Avendao, L. Esteva, J. Florez, J. Fuentes, G. García, G. Gómez, J. López,

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

Medicine and Biology. 2007 24(1):35-56. 32

P. Baloni, S. Ghosh, N. Chandra, Systems Approaches to Study Infectious Diseases,

Systems and Synthetic Biology, Springer, pp 151-172. 32

R. Shi, Y. Li and S. Tang, A mathematical model with optimal controls for cellular

immunology immunology of tuberculosis, Taiwanese Journal of mathematics, April 2014

(2):575-597. 32

A. Bru, P-J.Cardona, Mathematical Modeling of Tuberculosis Bacillary Counts and

Cellular Populations in the Organs of Infected Mice, PLoS ONE, 2014 5(9): e12985.

doi:10.1371/journal.pone.0012985. 32

H.M. Yang, Mathematical Modelling of the Interaction between Mycobacterium tuberculosis

Infection and Cellular Immune Response. In (Editor R. Mondaini): Proceedings

of BIOMAT 2011 (Santiago, Chile). World Scientific: Singapore: 309-330 (ISBN 13

-981-4343-42-8) 32

E. Guirado and LS. Schlesinger, Modeling the Mycobacterium tuberculosis granulomathe

critical battlefield in host immunity and disease, Frontier in immunology, 2013

(98): 1-7. 32

RV. Carvalho, J. Kleijn, AH. Meijer, and FJ. Verbeek, Modeling Innate Immune Response

to Early Mycobacterium Infection, Computational and Mathematical Methods

in Medicine, Volume 2012, 1-12. Article ID 790482. . 32

S. Goutelle, L. Bourguignon, RW. Jelliffe, J. E. Conte Jr., P. Maire, Mathematical

modeling of pulmonary tuberculosis therapy: Insights from a prototype model with

rifampin, Journal of Theoretical Biology, 2011(282): 8092. 32

E. Pienaar and M. Lerm, A mathematical model of the initial interaction between Mycobacterium

tuberculosis and macrophages, Journal of Theoretical Biology, 2014(342):

32

DG. Russell, Who puts the tubercle in tuberculosis?, Nat. Rev. Microbiol. 2007;5:39-47.

M. Nowak, R. May, Virus Dynamics, Oxford University Press, New York, 2000. 33

M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology.

Mathematical Biosciences. 1995 Febreary 125(2):155-164. 33

P. de Leenheer, HL. Smith. Virus Dynamics: a Global Analysis. SIAM J. Appl. Math.

(63):1313-1327. 33

A. Korobeinikov . Global Properties of Basic Virus Dynamics Models. Bull. Math. Biol.

a(66):879-883. 33

R. Van Crevel, T. Ottenhoff, J. Van der Meer. Innate Immunity to Mycobacterium

tuberculosis.American Society for Microbiology. 2002 15(2):294-309. 34, 40

J. Hale, Ordinary Differential Equations, Wiley, New York, 1969. 35


Enlaces refback

  • No hay ningún enlace refback.