Hindawi Publishing Corporation Computational and Mathematical Methods in Medicine Volume 2011, Article ID 325470, 13 pages doi:10.1155/2011/325470 Research Article Noninvasive Monitoring of Hepatic Damage from Hepatitis C Virus Infection J. Alavez-Ram´ ırez, 1 J. L. Fuentes-Allen, 2 and J. L ´ opez-Estrada 3 1 Divisi´ on Acad´ emica de Ciencias B´ asicas, Universidad Ju´ arez Aut´ onoma de Tabasco, Cunduac´ an, 86690 M´ exico, TAB, Mexico 2 Hospital de Infectolog´ ıa, Centro M´ edico Nacional la Raza, Instituto Mexicano del Seguro Social, 01200 M´ exico, DF, Mexico 3 Departamento de Matem´ aticas, Facultad de Ciencias, Universidad Nacional Aut´ onoma de M´ exico, 04510 M´ exico, DF, Mexico Correspondence should be addressed to J. Alavez-Ram´ ırez, jalavezrg@gmail.com Received 27 November 2009; Accepted 16 December 2010 Academic Editor: Brian D. Sleeman Copyright © 2011 J. Alavez-Ram´ ırez 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. The mathematical model for the dynamics of the hepatitis C proposed in Avenda˜ no 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. 1. Introduction Hepatitis C virus (HCV) infection represents a serious problem of public health with strong clinical and eco- nomic repercussions. Lethal consequences may arise from a subclinical acute infection followed by a latent period, and eventually hepatic cirrhosis (from 20% to 30% of the cases) or to hepatocellular carcinoma (with a far smaller percentage) [1], as final events at the end stage of chronic liver disease. It was not before 1989, that the infectious viral agent was identified as HCV in patients with hepatitis not A and not B [2]. At present, six different genotypes of HCV have been identified with diverse biological and clinical behaviors. For instance, it has been observed that genotype 1 response to therapy is less effective than one by genotypes 2 and 3 [3]. The most frequent ways for HCV transmission are blood transfusion, use of intravenous drugs, hemodialysis, tattoos, high-risk sexual behavior, occupational exposition of medical and paramedical personnel, vertical transmission from mother to her product, and organ transplants from an infected donor. It is important to say that the mechanism for HCV transmission is unidentified in a high percentage of patients (from 20% to 40%) [4]. The incubation period of HCV is 50 days in average, ranging from 15 to 150 days [2]. Factors influencing the rate of progression from chronic hepatitis to cirrhosis appear to include age at time of exposure, duration of infection, degree of previous liver damage, immunological system status, and HCV genotype. The disease progression is insid- ious; the clinically significant time of evolution varies: the diagnosis of chronic hepatitis, cirrhosis, and hepatocellular carcinoma have been estimated to be 10, 20, and 30 years, respectively [1, 5]. The majority of patients show increased levels of aminotransferases as well as hepatocellular damage. Bleeding of esophageal varices, ascitis, coagulopathy, and