THÔNG BÁO  

Kính mời quý Thầy, Cô Giảng viên, Nghiên cứu sinh, Học viên cao học, Sinh viên Khoa Toán - Ứng dụng và các bạn yêu thích Toán học quan tâm đến tham dự Seminar Giải tích của Prof. Gaël Raoul,

Đại học Ecole Polytechnique, Pháp.

Seminar được diễn ra tại phòng HB305, Trường Đại học Sài Gòn (273 An Dương Vương, Quận 5) trong 2 buổi:

Buổi 1: Từ 10g đến 11g00, thứ 2, ngày 27/6/2022

• Monday, June 27^th, 2022, 10AM-11AM, Room: HB305

Title: Wasserstein distance methods for a kinetic model from evolutionary biology

Abstract: We consider a population structured by a phenotypic trait. If the species reproduces sexually, when two parents produce an offspring, the trait of the offspring is a combination of the parent’s traits. The distribution of the offspring’s trait is given by the so-called infinitesimal model. We obtain the a reproduction term that is similar to a collision operator in kinetic theory. This reproduction term is associated to a multiplicative operator that represents natural selection. In this talk, we will consider the long time dynamics of solutions of that model when the selection is assumed weak enough. We will be able to show how estimates based on the Wasserstein distance can be used to extend approaches used by population geneticists.

Buổi 2: Từ 10g đến 11g00, thứ 3, ngày 28/6/ 2022

• Tuesday, June 28^th, 2022, 10AM-11AM, Room: HB305

Title: Propagation of pathogens in a heterogeneous environment and emergence of multi-resistant strains

Abstract: We consider a population that is structured by a phenotypic trait and a spatial variable. We will consider three strains (ie three possible trait values): resistance to a treatment A, resistance to a treatment B and resistance to both A and B (with a fitness cost for that last one). The treatments A and B will be alternated in space, and analyse the effect of this spatial heterogeneity on the propagation of the pathogen population. Several propagation strategies can be used by the pathogen to propagate in space: the propagation can for instance be driven by a specialist type, or by the multi-resistant. The main outcomes of this study are the following:

- Through the use of propagation speed argument, we are able to discuss the emergence of multi-resistant strains at the edge of an epidemics, and show that propagation situations are more favourable than steady scenario for the development of these dangerous pathogen.

- We show that a good understanding of the dynamics of simple population models can provide useful tools to consider complex situations.

Finally, I will discuss some theoretical developments on stochastic propagation models that provide exciting perspectives on these questions.