Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 325470, 13 pages
doi:10.1155/2011/325470
Research Article

Noninvasive Monitoring of Hepatic Damage from Hepatitis C Virus Infection

1División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Cunduacán, 86690 México, TAB, Mexico
2Hospital de Infectología, Centro Médico Nacional la Raza, Instituto Mexicano del Seguro Social, 01200 México, DF, Mexico
3Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México, DF, Mexico

Received 27 November 2009; Accepted 16 December 2010

Academic Editor: Brian D. Sleeman

Copyright © 2011 J. Alavez-Ramírez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The mathematical model for the dynamics of the hepatitis C proposed in Avendaño et al. (2002), with four populations (healthy and unhealthy hepatocytes, the viral load of the hepatitis C virus, and T killer cells), is revised. Showing that the reduced model obtained by considering only the first three of these populations, known as basic model, has two possible equilibrium states: the uninfected one where viruses are not present in the individual, and the endemic one where viruses and infected cells are present. A threshold parameter (the basic reproductive virus number) is introduced, and in terms of it, the global stability of both two possible equilibrium states is established. Other central result consists in showing, by model numerical simulations, the feasibility of monitoring liver damage caused by HCV, avoiding unnecessary biopsies and the undesirable related inconveniences/imponderables to the patient; another result gives a mathematical modelling basis to recently developed techniques for the disease assessment based essentially on viral load measurements.