Phénomènes de propagation et d’organisation spatiale en biologie

Journée thématique interdisciplinaire maths-bio

Université Paris-Dauphine, 29 et 30 novembre 2022, salle A709 (dans le cadre des réseaux MEDIA / A2 du département mathnum INRAE)

Programme :

Mardi 29 novembre, après-midi

13h30-14h : Accueil, espace 7 (7^e étage, aile A).

14h-17h : Exposés, salle A709.

• Vincent Bansaye (CMAP, École Polytechnique) Processus de branchement et épidémie pour de grandes métapopulations .

  Nous nous intéresserons à une population structurée spatialement par un processus ponctuel de Poisson. Nous expliquerons d'abord comment construire le processus qui combine déplacement, naissance, mort et infection, en autorisant une condition initiale non bornée. L'objectif de l'exposé sera ensuite d'obtenir des approximations dans un régime diffusif, impliquant une homogénéisation stochastique pour le mouvement.
  Travail en collaboration avec Michele Salvi (Roma)

• Cécile Taing (LMA, Université de Poitiers).

Pause café, espace 7 (7^e étage, aile A).

• Léna Klay (Sorbonne Université). Spatial spread of suppression and eradication drives.

  Understanding the temporal spread of gene drive alleles (alleles that disrupt the laws of heredity by biasing their own transmission) through modeling is essential before any field experiments. And taking into account spatial structure and demography is a step towards more realistic models. In this talk, I will present results from a deterministic reaction-diffusion model, describing the interplay between demographic and allelic dynamics. I will address the following questions: Does the drive invade the wild-type population? If it does, then at which speed? What are the demographic consequences? Under certain conditions, we observe the existence of a release threshold: the drive alleles only spreads when the number of introduced individuals is large enough. In contrast with non-spatial models, the value of the threshold depends on demographic parameters. We also note that an eradication drive is able to spread in the population, leading to global extinction. However to do so, it must counteract a demographic flux, which can sometimes hamper its spread. In a second part, I will consider various timings of gene conversion (considering conversion can happen in the zygote or in the germline) and different probabilities of gene conversion (instead of assuming 100% conversion). Numerical simulations show intriguing results: in some cases without release threshold, the speed of invasion and the final allele proportions appear to be fully independent upon demographic parameters. I will present preliminary analytical results supporting these heuristic findings and put into perspective the necessity of considering demographic dynamics in the models.

Mercredi 30 novembre, matin

9h-12h : Exposés, salle A709.

• Bertrand Cloez (MISTEA, Inrae, Montpellier).

Pause café, espace 7 (7^e étage, aile A).

• Hélène Hivert (Centrale Lyon) : Numerical schemes for concentration phenomena in Lotka-Volterra equations.

  We consider a population structured in phenotypic trait, which influcences the adaptation of individuals to their environment. Each individual has the trait of his parent, up to small mutations. When considered in a regime of long time and small mutation, and with appropriate hypothesis, the distribution of the population is expected to concentrate at some dominant traits. Dominant traits can also evolve in time, thanks to mutations. From a technical point of view, the concentration phenomenon is described thanks to a Hopf-Cole transform in the model. The asymptotic regime is a constrained Hamilton-Jacobi equation. Because of the lack of regularity of the constraint, it can indeed have jumps, its numerical approximation must be carefully discussed. We propose a framework for the discretization of the limit equation, and asymptotic-preserving schemes for the original problem transformed with Hopf-Cole.

• Jérome Coville (BioSP, Inrae) : On stochastic modelling of vector borne epidemic and the evolutionary processes of the pathogen dispersed at the scale of a field.

  I will present a stochastic model we have built to describe the evolution of a pathogen that disperses in a field during an epidemic event and where transmission is by made through vectors. After a brief introduction of the motivations, I will present the model and the different asymptotics that can be obtained.

12h: Repas convivial, espace 7 (7^e étage, aile A).

Organisateurs : Florian Patout, Raphaël Forien, Emeric Bouin, Amic Frouvelle.

Participant·e·s : .