A MARKOV MODEL FOR THE SPREAD OF HEPATITIS C VIRUS

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. hal-00320363, version 3- 19 Feb 2010 1. Motivations Hepatitis C virus (HCV) infects 170 million people in the world (3 % of the population) and 9 million in Europe (1 % of the population) [16]. More than 75 % of newly infected patients progress to develop chronic infection. Then, Cirrhosis develops in about 10 % to 20 %, and liver cancer develops in 1 % to 5 % over a period of 20 to 30 years. These long-term consequences, which suggest an increase

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Hepatitis C treatment as prevention of viral transmission and liver-related morbidity in persons who inject drugs

International audienceHepatitis C virus (HCV) seroprevalence remains high in people who inject drug (PWID) populations, often above 60%. Highly effective direct-acting antiviral (DAA) regimens (90% efficacy) are becoming available for HCV treatment. This therapeutic revolution raises the possibility of eliminating HCV from this population. However, for this, an effective cascade of care is required. In the context of the available DAA therapies, we used a dynamic individual-based model including a model of the PWID social network to simulate the impact of improved testing, linkage to care, and adherence to treatment, and of modified treatment recommendation on the transmission and on the morbidity of HCV in PWID in France. Under the current incidence and cascade of care, with treatment initiated at fibrosis stage ≥F2, HCV prevalence decreased from 42.8% to 24.9% (95% confidence interval: 24.8-24.9) after 10 years. Changing treatment initiation criteria to treat from F0 was the only intervention leading to a substantial additional decrease in prevalence, which fell to 11.6% (95% CI: 11.6-11.7) at 10 years. Combining this change with improved testing, linkage to care, and adherence to treatment decreased HCV prevalence to 7.0% (95% CI: 7.0-7.1) at 10 years and avoided 15% (95% CI: 14-17) and 29% (95% CI: 28-30) of cirrhosis complications over 10 and 40 years, respectively. Conclusions: Major decreases in prevalent HCV infections occur only when treatment is initiated at early stages of fibrosis, suggesting that systematic treatment in PWID, where incidence remains high, would be beneficial. However, elimination within the 10 next years will be difficult to achieve using treatment alone, even with a highly improved cascade of care. (Hepatology 2016;63:1090–1101