Mathematical Biosciences and Engineering, 2013, 10(4): 1045-1065. doi: 10.3934/mbe.2013.10.1045

Primary: 34D20, 92D30; Secondary: 65L20, 93C15.

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Model for hepatitis C virus transmissions

1. Merck Research Laboratories, UG1C-60, PO Box 1000, North Wales, PA 19454-1099

Hepatitis C virus (HCV) is a leading cause of chronic liver disease. Thispaper presents a deterministic model for HCV infection transmission and usesthe model to assess the potential impact of antiviral therapy. The model isbased on the susceptible-infective-removed-susceptible (SIRS) compartmentalstructure with chronic primary infection and possibility of reinfection.Important epidemiologic thresholds such as the basic and controlreproduction numbers and a measure of treatment impact are derived. We findthat if the control reproduction number is greater than unity, there is alocally unstable infection-free equilibrium and a unique, globallyasymptotically stable endemic equilibrium. If the control reproductionnumber is less than unity, the infection-free equilibrium is globallyasymptotically stable, and HCV will be eliminated. Numerical simulationssuggest that, besides the parameters that determine the basic reproductionnumber, reinfection plays an important role in HCV transmissions andmagnitude of the public health impact of antiviral therapy. Further,treatment regimens with better efficacy holds great promise for lowering thepublic health burden of HCV disease.
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