  We propose a Markov model for the spread of Hepatitis C virus (HCV) among
drug users who use injections. We then proceed to an asymptotic analysis (large
initial population) and show that the Markov process is close to the solution
of a non linear autonomous differential system. We prove both a law of large
numbers and functional central limit theorem to precise the speed of
convergence towards the limiting system. The deterministic system itself
converges, as time goes to infinity, to an equilibrium point. This corroborates
the empirical observations about the prevalence of HCV.
