Mathematical Biosciences and Engineering (MBE)

Model for hepatitis C virus transmissions

Pages: 1045 - 1065, Volume 10, Issue 4, August 2013      doi:10.3934/mbe.2013.10.1045

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Elamin H. Elbasha - Merck Research Laboratories, UG1C-60, PO Box 1000, North Wales, PA 19454-1099, United States (email)

Abstract: Hepatitis C virus (HCV) is a leading cause of chronic liver disease. This paper presents a deterministic model for HCV infection transmission and uses the model to assess the potential impact of antiviral therapy. The model is based on the susceptible-infective-removed-susceptible (SIRS) compartmental structure with chronic primary infection and possibility of reinfection. Important epidemiologic thresholds such as the basic and control reproduction numbers and a measure of treatment impact are derived. We find that if the control reproduction number is greater than unity, there is a locally unstable infection-free equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the control reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable, and HCV will be eliminated. Numerical simulations suggest that, besides the parameters that determine the basic reproduction number, reinfection plays an important role in HCV transmissions and magnitude of the public health impact of antiviral therapy. Further, treatment regimens with better efficacy holds great promise for lowering the public health burden of HCV disease.

Keywords:  HCV, treatment, reinfection, mathematical model, global stability, endemic equilibrium, reproduction number.
Mathematics Subject Classification:  Primary: 34D20, 92D30; Secondary: 65L20, 93C15.

Received: October 2012;      Accepted: March 2013;      Available Online: June 2013.