The Open MAMBA Seminar is an internal seminar open to all which takes place once every month at INRIA Paris. The talks are given by PhD/post-docs with the following goals:
- Reinforce the team spirit by centering the talks on MAMBA (extended) students works
- Bring more math-bio at the INRIA center (in complement with the INRIA-LJLL meetings)
- Favor scientific exchanges on current projects, each talk being followed by an (informal) discussion between researchers.
The seminar takes place once every month on mondays from 1:30 to 3 pm. It is composed of two talks of 30mn, each followed by 15mn discussions.
INRIA Paris, 2 rue Simone Iff (see How to reach), Room ‹‹ Jacques-Louis Lions ››, bâtiment C
NB: An ID card is necessary to enter the building
Diane Peurichard: firstname.lastname@example.org
Dirk Drasdo: email@example.com
Monday, march 19:
Title: Measure solution for the classical size-equation with linear growth rate
Abstract: In a recent paper, E. Bernard, M. Doumic and P. Gabriel showed the existence of a cyclic asymptotic bahaviour of the solution of the size-equation with linear growth rate in a weighted L^2 space which consists in a Fourier serie built on the eigenfunctions of the model. On another hand, P. Gabriel recently solved the age Equation and showed a relation with the related principal eigenfunction. We are now wondering how this behaviour appear for measure solutions in the case of the size Equation. After defining what a measure solution to a PDE is, I will explain the semigroups methods we attempt to use to obtain the desired result and the difficulties we are already facing.
2. Camille Pouchol
Title: Dirichlet control towards steady states for the 1D monostable and bistable equations
Abstract: I will talk about the problem of controlling parabolic semilinear equations arising in population dynamics, namely the 1D monostable and bistable equations on (0,L) for a density of individuals between 0 (extinction) and 1 (invasion), by means of Dirichlet controls between 0 and 1. I will explain why driving the system towards 0 or 1 asymptotically is always possible for the state 1, and for 0 as well if L is below some threshold value, computable by phase plane analysis. In the bistable case, I will prove that the other homogeneous steady state 0 < θ < 1, though unstable for the corresponding ODE, can be reached in finite time. The central tools are the phase portrait for the stationary problem, the parabolic maximum principle, and the staircase method in control theory.
Monday, february 12:
1. Mathieu Mezache:
2. Martin Strugarek
Title: Mosquito population replacement: an optimal control viewpoint
(in collaboration with Luis Almeida, Yannick Privat (LJLL) and Nicolas Vauchelet (LAGA))
Abstract: Transinfection of Wolbachia bacteria is currently used in wild Aedes populations to suppress these mosquitoes’ ability to transmit some viruses (vector competence), in particular dengue viruses. This recently developed technique relies on the mass rearing and release of lab-infected individuals of both sexes. The introduced phenotype can replace the wild one thanks to an asymmetric sterile crossing known as cytoplasmic incompatibility (CI). It is expected to practically stop disease circulation and be very cost-efficient as the Wolbachia infection will maintain once established over many generations, thanks to almost perfect vertical transmission from mother to offspring. Our work aims at improving these so-called “Wolbachia population replacement strategies”, using mathematical modeling to design the release sizes and timings (and, in future, locations). Here, we formulate this as an optimal control problem for an ODE system and prove qualitative properties of the optimal strategies under resource constraints. Numerical simulations illustrate these results. We also recover a bistable scalar equation on the proportion of infected individuals by a proper scaling of the parameters, and rigorously prove the convergence of the optimization problems to a limit problem for which uniqueness and explicit solution are established.
Monday, january 22:
1. Yi Yin:
2. Jieling Zhao: