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3-5 déc. 2025 Paris (France)
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Presentation This workshop aims at bringing together several experts of different fields of mathematical biology, in order to explore new results and new research directions, from population dynamics to kinetic modelling of ecosystems and game theory . It will take place in Amphitheatre Hermite, Institut Henri Poincaré, Paris, from the 3rd to the 5th of December. Program
Wednesday 3/12
Support Organizers : Idriss Mazari (Ceremade, univ. Paris Dauphine), Grégoire Nadin (Institut Denis Poisson, univ. Orléans) With support from: Sorbonne Université, LJLL (Emergence grant), Paris Dauphine Université PSL, CEREMADE (PSL Young Researcher Grant), Institut Henri Poincaré. Abstracts This section will be updated regularly. Elisa Affili (LMRS, Université de Rouen Normandie) Controllability in Lotka-Volterra competitive systems with constrained controls We are interested in controlling the asymptotic behaviour of two competing species in an interval by controlling the size of the populations at the boundary. In particular, we want to know if it is possible to eradicate one of the species. Since the boundary controls have to satisfy some constraints, classic techniques in control theory cannot be applied. In this talk, we will discuss non-controllability phenomena due to the presence of barrier solutions depending on the length of the interval and the competition coefficients of the systems.
Aniket Banerjee (Laboratoire Jacques-Louis Lions, Sorbonne Université) Effect of climate change and bio-control strategies on agricultural pest population Soybean aphids are an invasive pest that significantly impact soybean production. Although genetically modified soybean varieties have been developed to resist infestation, aphid feeding can modify plant physiology, increasing susceptibility to further colonization. This vulnerability arises through two key mechanisms—feeding facilitation and obviation of resistance—and is influenced by both seasonal conditions and climate change. We use a mathematical model that captures these biological interactions through a non-local population framework and includes non-smooth Allee effects within a two-species Lotka–Volterra competition model. We explore various bio-control strategies and demonstrate how aphid populations can be regulated. In particular, providing additional food resources in agricultural patches emerges as an effective approach to reduce pest pressure.
Laura Kanzler (Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Université) Greta Lamonaca (Institut Denis Poisson, Université d'Orléans) Mean Field Models in Spatial Ecology
In this presentation we qualitatively explore the role of human actions in the decline of biodiversity, focusing on the problem of fishing in a bounded domain. More precisely, we consider a population of fishermen whose actions influence, and are influenced by, the dynamics of a fish population. Two distinct scenario are considered: in the framework of the Mean Field Game (MFG), fishermen act competitively to maximize their individual income, while in the context of Mean Field Control (MFC) they cooperate under a central planner to maximize a common objective. We will combine reaction diffusion equations and MFG theory to model and analyze the two fishing systems.
Although we present our framework in the context of fisheries, the conceptual approach could be applied to other resource management problems such as agriculture or logging. Our analysis focuses mainly on ergodic (static) regimes, which provide a simpler context for investigating basic properties. Particular attention is given to the comparison between MFG and MFC: we will present some assumptions under which the Lasry-Lions monotonicity condition holds (and so, uniqueness of solutions), other regimes where, instead, multiple solutions occur and the variables that seem to determine these different phenomena. This work was carried out in collaboration with Idriss Mazari and Grégoire Nadin.
David Nahmani (LAGA, univ. Sorbonne Paris Nord)
Jean-Christophe Poggiale (Institut Pytheas, Aix-Marseille university) Managing risks and trade-offs in multispecies fisheries: the role of trophic control and price asymmetry Ecosystem-based fisheries management (EBFM) aims to balance ecological and economic goals while employing precautionary measures to address uncertainties in knowledge and management. This study investigates fishing strategies to achieve this balance while minimizing the associated risks. Using a simplified prey-predator model, we explored various scenarios reflecting the diversity of global fisheries. The model integrates key ecological dynamics (bottom-up and top-down forces), economic factors (price structures), and aggregates the diversity of fishing practices by distributing fishing mortality across species. Our findings reveal that predators are always more affected by fishing than prey, regardless of the effort distribution. High yields are achieved by reducing predator densities—either maximizing predator catches when they are highly valued or reducing predation pressure to enhance prey harvests when prey prices are high. Such strategies result in significant ecological impacts, leading to systematic trade-offs. Elevated prey prices and top-down controlled systems intensify these trade-offs, increasing ecological risks. Regarding uncertainties, we demonstrate that maximizing yields poses risks to both biodiversity and profitability. Reconciliation is challenging but feasible when both species are fished. This balance can be achieved only in bottom-up controlled systems where prey valuation is not disproportionately high compared to predator prices.
Nicolas Vauchelet (LAGA, univ. Paris Nord) Mathematical analysis of a ‘rolling carpet’ strategy for the sterile mosquito technique This work has been done in collaboration with Luis Almeida, Alexis Leculier, and Nga Nguyen.
Chiara Villa (MAP5, Université Paris Cité) New trends in PDE models for heterogeneous cell populations Heterogeneity and plasticity in individual cell behaviour play a fundamental role in developmental and pathological (e.g. cancer) processes. The phenotype of cell, i.e. the ensemble of its observable characteristics determining its behaviour, can be quantified by the level of expression of certain genes or proteins in the cell, which are typically measured on a continuum. For this reason, nonlinear integro-differential equations describing the evolutionary and spatiotemporal dynamics of phenotype-structured cell populations have become increasingly popular in the mathematical community. In particular, in the past 20 years much effort has been put into the analysis of formal asymptotic behaviour in well-mixed and spatially-explicit models, and more recently new interdisciplinary problems emerged in the quest to calibrate these models with experimental data. This talk will provide an overview of the field, covering basics, new trends and open questions on both the mathematical and interdisciplinary fronts. |
