Modelling hepatitis C virus infection and the development of hepatocellular carcinoma

While mathematical models exist describing the dynamics of hepatitis C virus (HCV), most of them focus on the short term dynamics after the commencement of antiviral therapy. This work is the first attempt at mathematically modelling the full course of HCV infection and the impact that these viral and immune processes have on the progression to hepatocellular carcinoma (HCC). This model is based on the premise that these long term conditions are ultimately random and likely driven by the cell-mediated immune response. The risk of cancer arising is modelled through a stochastic model that incorporates the dynamics of HCV over the course of infection. Our model simulations produce approximately 9% prevalence of HCC in individuals after 40 years, consistent with the literature estimates. We find that higher viral infectivity leads to a greater likelihood of developing HCC (p<0.0001), but it does not determine the speed with which it arises. This infectivity drives the level of immune response, the amount of hepatocyte proliferation, and the risk of a mutational event. In our simulations the probability of developing HCC increases approximately linearly with duration of infection at the rate of 2.4 incident cases per thousand HCV-infected person years. This indicates that the sooner viral replication can be suppressed through antiviral therapy, the greater the chance of forestalling HCC.