Abstract
There are two mathematical models of Hepatitis C virus (HCV) being discussed; the original model of HCV viral dynamics (Neumann et al., 1998) and its extended model (Dahari et al., 2007). The key aspects of the mathematical models have provided resources for analysing the stability of the uninfected and the infected steady states, in evaluating the antiviral effectiveness of therapy and for estimating the ranges of values of the parameters for clinical treatment. The original model is considered to be a deterministic model because of the predictive nature of the antiviral therapy within the constant target cells. Numerical simulations are carried out in the extended model, to explain the stability of the steady states in the absence or existence of migration in hepatocytes and, drug efficacy in treating HCV infection.
Highlights
Hepatitis C virus (HCV) infection is a major primary cause of chronic liver disease, liver cancer and liver cirrhosis
Once infected, the cell death rate exhibits large lifespan variation with half-life between 1.7 and 70 days. This implies that early monitoring of viral load is essential to control HCV infection through faster killing of infected cells with interferon - α (IFN)-α doses of 10 and 15 million international units daily; standard current dose is between 3 to 15 mIU (Neumann et al, 1998)
Our studies focus on the original model of HCV infection under therapy (Neumann et al, 1998), where we present results for the stability of both the uninfected and infected steady states, and compare the behaviour of the original model to the extended model (Dahari et al, 2007) that account for the ultimate HCV elimination
Summary
Hepatitis C virus (HCV) infection is a major primary cause of chronic liver disease, liver cancer and liver cirrhosis. Once infected, the cell death rate exhibits large lifespan variation with half-life between 1.7 and 70 days This implies that early monitoring of viral load is essential to control HCV infection through faster killing of infected cells with IFN-α doses of 10 and 15 million international units (mIU) daily; standard current dose is between 3 to 15 mIU (Neumann et al, 1998). Upon therapy cessation, approximately 50% of treated HCV patients exhibited a rebound of viral plateau, to pretreatment levels that define whether, the antiviral therapy is only partially effective during treatment phase or will it be successful in eradicating HCV. In order to accomplish these goals, the models and their parameters are presented and described, followed by linear stability analysis of the models to examine the asymptotic stability of each their steady states
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