Dinámica del virus de la hepatitis C con carga viral y ALT y monitoreo del daño hepático libre de biopsias

Main Article Content

Justino Alavez-Ramírez


hepatitis C, viral load, hepatic damage, biopsies, parameters, threshold parameter.


The standard model of three populations (healthy and unhealthy hepatocytes, and viral load) for the study of the dynamics of hepatitis C virus (HCV), is compared with viral dynamic model with alanine aminotransferase (ALT). In terms of the threshold parameter that it’s the same for both models, the existence and local asymptotic stability of the endemically infected equilibrium steady state, and the global stability of the healthy individual equilibrium steady state are established. Furthermore, an experimental study is presented showing that it’s possible to carry out the monitoring of hepatic damage biopsies free by numerical parameter estimation, considering only viral load and ALT levels measurements and a reasonable assessment of pretreatment hepatic damage.

PACS: 87.19.xd

MSC: 97M60


Download data is not yet available.
Abstract 557 | PDF (Español) Downloads 281


[1] B.A. Cipra. Will Viruses Succumb To Mathematical Models? SIAM News, 32(2), 1999.

[2] Hepatitis C. Informe de PKID, http://www.pkids.org/Spa phrhcv.pdf, Octubre de 2005.

[3] A.U. Neumann, N.P. Lam, H. Dahari, D.R. Gretch, T.E. Wiley, T.J. Layden, A.S. Perelson. Hepatitis C Viral Dynamics in Vivo and the Antiviral Efficacy of Interferon-_ Therapy. Science, 282(5386), 103-107 (1998).

[4] T. Poynard, P. Marcellin, S.S. Lee, C. Niederau, G.S. Minuk, G. Ideo, V. Bain, J. Heathcote, S. Zeuzem, C. Trepo, J. Albrecht. Randomised trial of interferon _2b plus ribavirin for 48 weeks or 24 weeks versus interferon _2b plus placebo for 48 weeks for treatment of chronic infection with hepatitis C virus. The Lancet, 352(9138), 1426-1432 (1998).

[5] El Hígado. Informe de PKID, http://www.pkids.org/Spa phrliv.pdf, Septiembre de 2004.

[6] J. Alavez-Ramírez, J.L. Fuentes-Allen, Je. López-Estrada. Monitoreo del daño hepático causado por el VHC sin necesidad de Biopsias. Por publicar, 2005.

[7] R. Avendaño, L. Esteva, J.A. Flores, J.L. Fuentes-Allen, G. Gómez, Je. López- Estrada. A Mathematical Model for the Dynamics of Hepatitis C. J. of Theoretical Medicine, 4(2), 109-118 (2002).

[8] R.M. Ribeiro, J. Layden-Almer, K.A. Powers, T.J. Layden, A.S. Perelson, Dynamics of Alanine Aminotrasnferase During Hepatitis C Virus Treatment. Hepatology, 38(2), 509-517 (2003).

[9] L. Edsberg, P.-°A. Wedin. Numerical tools for parameter estimation in ODEsystems. Optimization Methods and Software, 6, 193-217 (1995).

[10] P. Hartman. Ordinary Differential Equations, 2nd edition, Boston: Birkhauser Verlag, 1982.