A Markov model for the spread of Hepatitis C

Laure Coutin (1) , Laurent Decreusefond (2) , Jean-Stephane Dhersin (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LTCI - Laboratoire Traitement et Communication de l'Information

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.

Mots clés: Epidemiology; HCV; Markov processes; mean field approximation

Domaines: Probabilités [math.PR]

Laure Coutin, Laurent Decreusefond, Jean-Stephane Dhersin. A Markov model for the spread of Hepatitis C. 2008. ⟨hal-00320363v1⟩