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- J-F Delmas, L. Marsalle, V. C. Tran
- 2010

We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton-Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring locations depend on the position of the mother and the number of offspring. We prove a law of large numbers for the… (More)

- Michael G B Blum, Viet Chi Tran
- Biostatistics
- 2010

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian computation (ABC), an alternative to data imputation methods such as Markov chain Monte Carlo (MCMC) integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on… (More)

UNLABELLED
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… (More)

- Sylvain Billiard, Viet Chi Tran
- Journal of mathematical biology
- 2012

Disentangling the processes leading populations to extinction is a major topic in ecology and conservation biology. The difficulty to find a mate in many species is one of these processes. Here, we investigate the impact of self-incompatibility in flowering plants, where several inter-compatible classes of individuals exist but individuals of the same class… (More)

- Sylvie Méléard, Viet Chi Tran
- Journal of mathematical biology
- 2009

We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump process that generalizes the Trait… (More)

- Stéphan Clémençon, Viet Chi Tran, Hector de Arazoza
- Journal of biological dynamics
- 2008

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals… (More)

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age,… (More)

A superprocess limit for an interacting birth-death particle system modelling a population with trait and age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while ages are set to zero. Because of interactions between individuals, standard approaches based on the Laplace transform do not… (More)

We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested… (More)

Statistical inference with missing data is a recurrent issue in epidemiology where the infection process is only partially observable. In this paper, Approximate Bayesian Computation, an alternative to data imputation methods such as Monte Carlo Markov chain integration, is proposed for making inference in epidemiological models. This method of inference is… (More)