A Markov model for the spread of Hepatitis C

TL;DR

This paper introduces a Markov model to analyze the spread of Hepatitis C among injection drug users, providing theoretical insights into its dynamics and long-term behavior.

Contribution

It develops a Markov model for HCV spread, analyzes its asymptotic behavior, and proves convergence to an equilibrium, linking stochastic processes to deterministic systems.

Findings

Model closely approximates the spread dynamics of HCV.

Convergence to equilibrium explains empirical prevalence observations.

Provides theoretical foundation for HCV intervention strategies.

Abstract

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.