Stability analysis of an in-vivo hepatitis C dynamics model with therapy

Abstract

It is well known that hepatitis C virus (HCV) causes development of end-stage liver disease and hepatocellular carcinoma worldwide, in spite of advances in therapy and improved knowledge of viral factors relating to the disease evolution. In this paper, we review and analyze a deterministic mathematical model developed to assess the effect of antiviral drug on the in-vivo HCV dynamics. We computed the endemic equilibrium point (EE) and performed the stability analysis of the model equilibria using a derived threshold quantity well-known as the effective reproductive number, 𝑅𝑒. The analytical results indicate that the disease free equilibrium point (DFE) is locally asymptotically stable, and globally asymptotically stable by using Metzler Stability Theory, if 𝑅 𝑒 < 1. This implies that antiviral therapy absolutely eradicates the disease in this scenery. Also, we find that the endemic equilibrium point (EE) is globally asymptotically stable if 𝑅 𝑒 > 1 by using the Lyapunov Direct Method with LaSalle Invariance Principle. This implies that the disease still persists in the presence of antiviral therapy. Numerical simulations were performed to support the analytical results and the results verify that there is no coexistence of the DFE and EE points and that the model has unique equilibria. Thus, we recommend that the treatment of an individual with HCV infection should be well managed by optimizing therapy regimen such as choice of suitable drug type and combination, dosage and therapy period to stop the transmission by reducing strictly Re less than unity.