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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)

- 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)

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)

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)

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)

We consider a continuous time stochastic individual based model for a population struc-tured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and we view the process in the timescale of mutations. Using averaging techniques due to… (More)

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 timescale separation condition , we obtain a jump process that generalizes the Trait… (More)