Mathematical models in ecology and evolution

Collection Mathematical models in ecology and evolution

Organizer(s) Vincent Calvez, Florence Débarre, Jimmy Garnier and Amandine Véber
Date(s) 3/21/22 - 3/25/22
linked URL
00:00:00 / 00:00:00
18 25

Epidemics on large random metapopulations and homogenization

By Vincent Bansaye

Joint work with Michele Salvi.

We are interested in population dynamics and epidemics for large random metapopu-lations. The sites of the metapopulation are described by a Poisson point process on the plane and transition rates between the sites depend on their distances. In such a non-homogeneous context, when the number of sites in a given box becomes large, homo-genization occurs, leading to a non trivial di˙usion of coe°cient and spread of epidemics. Our motivations come from the spread of epidemics on networks (farms, cities, patches. . . ). We will introduce an individual-based model including births, deaths and contaminations. We will first justify the existence of such a stochastic process starting from a (spatially) unbounded population distribution, which requires to control what can come from large distances. We will then prove the convergence of the renormalized stochastic process to a reaction diffusion models, with homogenized di˙usion coefficients. We may discuss further new and multi-scaling or extensions to more complex large random graphs.

Information about the video

  • Date of recording 3/21/22
  • Date of publication 6/24/22
  • Institution IHP
  • Language English
  • Audience Researchers
  • Format MP4

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