Jean-Stéphane Dhersin

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

Hepatitis 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)

Large graph limit for an SIR process in random network with heterogeneous connectivity

We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz (2008).

Asymptotic results on the length of coalescent trees

We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

Dynamic modelling of hepatitis C virus transmission among people who inject drugs: a methodological review.

Equipment sharing among people who inject drugs (PWID) is a key risk factor in infection by hepatitis C virus (HCV). Both the effectiveness and cost–effectiveness of interventions aimed at reducing HCV transmission in this population (such as opioid substitution therapy, needle exchange programmes or improved treatment) are difficult to evaluate using field surveys. Ethical issues and complicated access to the PWID population make it difficult to gather epidemiological data. In this context, mathematical modelling of HCV transmission is a useful alternative for comparing the cost and effectiveness of various interventions. Several models have been developed in the past few years. They are often based on strong hypotheses concerning the population structure. This review presents compartmental and individual‐based models to underline their strengths and limits in the context of HCV infection among PWID. The final section discusses the main results of the papers.

On the total length of external branches for beta-coalescents

In this paper we consider the beta(2 − α, α)-coalescents with 1 < α < 2 and study the moments of external branches, in particular, the total external branch length of an initial sample of n individuals. For this class of coalescents, it has been proved that n α-1 T (n) →D T, where T (n) is the length of an external branch chosen at random and T is a known nonnegative random variable. For beta(2 − α, α)-coalescents with 1 < α < 2, we obtain lim n→+∞ n 3α-5 𝔼(L ext (n) − n 2-α𝔼T)2 = ((α − 1)Γ(α + 1))2Γ(4 − α) / ((3 − α)Γ(4 − 2α)).

Effectiveness and cost-effectiveness of interventions targeting harm reduction and chronic hepatitis C cascade of care in people who inject drugs: The case of France

Direct‐acting antivirals (DAAs) represent an opportunity to improve hepatitis C virus (HCV) care cascade. This combined with improved harm reduction interventions may lead to HCV elimination especially in people who inject drugs (PWID). We assessed the effectiveness/cost‐effectiveness of improvements in harm reduction and chronic hepatitis C (CHC) care cascade in PWID in France. We used a dynamic model of HCV transmission and CHC natural history and evaluated the following: improved needle/syringe programmes‐opioid substitution therapies, faster diagnosis/linkage to care, earlier treatment initiation, alone and in combination among active PWID (mean age = 36). Outcomes were as follows: life expectancy in discounted quality‐adjusted life years (QALYs); direct lifetime discounted costs; incremental cost‐effectiveness ratio (ICER); number of infections/reinfections. Under the current practice, life expectancy was 15.846 QALYs, for a mean lifetime cost of €20 762. Treatment initiation at F0 fibrosis stage alone was less effective and more costly than faster diagnosis/linkage to care combined with treatment initiation at F0, which increased life expectancy to 16.694 QALYs, decreased new infections by 37%, with a ICER = €5300/QALY. Combining these interventions with harm reduction improvements was the most effective scenario (life expectancy = 16.701 QALYs, 41% decrease in new infections) but was not cost‐effective (ICER = €105 600/QALY); it became cost‐effective with higher initial HCV incidence rates and lower harm reduction coverage than in our base‐case scenario. This study illustrated the high effectiveness, and cost‐effectiveness, of a faster diagnosis/linkage to care together with treatment from F0 with DAAs. This “Test and treat” strategy should play a central role both in improving the life expectancies of HCV‐infected patients, and in reducing HCV transmission.

Super Brownian motion with interactions

Using an approximating scheme with the Brownian snake, we prove the existence of solution to a martingale problem for super Brownian motion with interactions.

Lower functions for the support of super-Brownian motion

The aim of this paper is to describe the minimum speed at which a super-Brownian motion starting at the Dirac mass at 0 moves away from its initial point. More precisely, we consider the class of functions and then determine the values of [kappa] such that the support of super-Brownian motion exits the ball of radius [phi][kappa](t) before time t, for every t small enough.

Inferring R0 in emerging epidemics-the effect of common population structure is small.

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain. Here, we show that, for many common true underlying heterogeneous contact structures, the simplification to neglect such structures and instead assume that all contacts are made homogeneously in the whole population results in conservative estimates for R0 and the required control effort. This means that robust control policies can be planned during the early stages of an outbreak, using such conservative estimates of the required control effort.