arXiv subjects

Apolline Louvet

Publications and source records attributed to Apolline Louvet.

6 recordsLinked to original sources

arXiv2026

A new stochastic SIS-type modelling framework for analysing epidemic dynamics in continuous space

We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $Λ$-Fleming-Viot (SLFV) process. The model can be described by as little as three parameters, and is dual to a spatial branching process with competition linked to genealogies of infected individuals. Therefore, it is a possible modelling framework to develop computationally tractable inference tools for epidemics in a continuous space using demographic and genetic data.We provide mathematical constructions of the process based on well-posed martingale problems as well as driving space-time Poisson point processes. With these devices and the duality relation in hand, we unveil some of the drivers of the transition between extinction and survival of the epidemic. In particular, we show that extinction is in large parts independent of the initial condition, and identify a strong candidate for the reproduction number R 0 of the epidemic in such a model.

math.PR↗

arXiv2025

Effect of stochasticity on the growth of the infty-parent SLFV process

We explore the impact of different forms of stochasticity on the expansion dynamics of a stochastic growth model called the $\infty$-parent spatial $Λ$-Fleming Viot process. This process belongs to a family of population genetics processes in a spatial continuum, and was recently introduced to study the evolution of genetic diversity in spatially expanding populations. Its stochastic reproduction dynamics gives rise to a rich growth structure, on which first theoretical results were obtained. In this paper, we further explore this growth dynamics using two complementary approaches: an analytical study of a simplified model for growth at the front edge, and a simulation-based study. We show that the observed expansion speed is the result of the interplay of stochasticity in shapes, timings and locations of reproduction events, each form of stochasticity being necessary but not sufficient to explain the expansion dynamics. We also identify distinctive scaling regimes for the variance of hitting times by the front and the bulk of the expansion. Moreover, we obtain results on the scaling of the front fluctuations, which point towards the front interface belonging to the KPZ universality class.

math.PR↗

arXiv2024

Asymptotics for the growth of the infinite-parent Spatial Lambda-Fleming-Viot model

The infinite-parent spatial Lambda-Fleming-Viot (SLFV) process is a model of random growth, in which a set evolves by the addition of balls according to points of an underlying Poisson point process, and which was recently introduced to study genetic diversity in spatially expanding populations. In this article, we give asymptotics for the location and depth of the moving interface, and identify the exact asymptotic scale of the transverse fluctuations of geodesics. Our proofs are based on a new representation of the infinite-parent SLFV in terms of chains of reproduction events, and on the study of the properties of a typical geodesic. Moreover, we show that our representation coincides with the alternative definitions of the process considered in the literature, subject to a simple condition on the initial state. Our results represent a novel development in the study of stochastic growth models, and also have consequences for the study of genetic diversity in expanding populations.

math.PR↗

arXiv2023

Measure-valued growth processes in continuous space and growth properties starting from an infinite interface

The k-parent and infinite-parent spatial Lambda-Fleming Viot processes (or SLFV), introduced in Louvet (2023), form a family of stochastic models for spatially expanding populations. These processes are akin to a continuous-space version of the classical Eden growth model (but with local backtracking of the occupied area allowed when k is finite), while being associated to a dual process encoding ancestry. In this article, we focus on the growth properties of the area occupied by individuals of type 1 (type 0 encoding units of empty space). To do so, we first define the quantities that we shall use to quantify the speed of growth of the occupied area. Using the associated dual process and a comparison with a first-passage percolation problem, we show that the growth of the occupied region in the infinite-parent SLFV is linear in time. Because of the possibility of local backtracking of the occupied area, the result we obtain for the k-parent SLFV is slightly weaker. It gives an upper bound on the probability that a given location is occupied at time t, which also shows that growth in the k-parent SLFV is linear in time. We use numerical simulations to approximate the growth speed for the infinite-parent SLFV, and we observe that the actual speed may be higher than the speed expected from simple first-moment calculations due to the characteristic front dynamics.

math.PR↗

arXiv2022

Stochastic measure-valued models for populations expanding in a continuum

We model spatially expanding populations by means of two spatial $Λ$-Fleming Viot processes (or SLFVs) with selection: the k-parent SLFV and the $\infty$-parent SLFV. In order to do so, we fill empty areas with type 0 ''ghost'' individuals with a strong selective disadvantage against ''real'' type 1 individuals, quantified by a parameter k. The reproduction of ghost individuals is interpreted as local extinction events due to stochasticity in reproduction. When k $\rightarrow$ +$\infty$, the limiting process, corresponding to the $\infty$-parent SLFV, is reminiscent of stochastic growth models from percolation theory, but is associated to tools making it possible to investigate the genetic diversity in a population sample. In this article, we provide a rigorous construction of the $\infty$-parent SLFV, and show that it corresponds to the limit of the k-parent SLFV when k $\rightarrow$ +$\infty$. In order to do so, we introduce an alternative construction of the k-parent SLFV which allows us to couple SLFVs with different selection strengths and is of interest in its own right. We exhibit three different characterizations of the $\infty$-parent SLFV, which are valid in different settings and link together population genetics models and stochastic growth models.

math.PR↗

arXiv2022

Extinction threshold and large population limit of a plant metapopulation model with recurrent extinction events and a seed bank component

We introduce a new model for plant metapopulations with a seed bank component, living in a fragmented environment in which local extinction events are frequent. This model is an intermediate between population dynamics models with a seed bank component, based on the classical Wright-Fisher model, and Stochastic Patch Occupancy Models (SPOMs) used in metapopulation ecology. Its main feature is the use of "ghost" individuals, which can reproduce but with a very strong selective disadvantage against "real" individuals, to artificially ensure a constant population size. We show the existence of an extinction threshold above which persistence of the subpopulation of "real" individuals is not possible, and investigate how the seed bank characteristics affect this extinction threshold. We also show the convergence of the model to a SPOM under an appropriate scaling, bridging the gap between individual-based models and occupancy models.

math.PR↗