Non-Local Models Arising from Biology
Modèles non locaux issus de la biologie
11 – 15 October, 2021
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Scientific Committee
Comité scientifique José Antonio Carrillo (University of Oxford) |
Organizing Committee
Comité d’organisation Matthieu Alfaro (Université de Rouen Normandie) |
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Mathematical models based on partial differential equations are pervasive in understanding natural phenomena, and biology is no exception. It turns out that many phenomenological models in biology require, or benefit from, the introduction of so-called nonlocal terms which involve the behavior of the distribution function at several points, as opposed to the more common local terms involving derivatives. Several relevant examples in biology are concerned with the speed of propagation of species in ecology, selection-mutation models in evolutionary biology (in the context of climate change for instance), growth-fragmentation processes relevant for cells and aggregates, neural population models, segregation of species in ecology and biology, etc. These models share similar mathematical difficulties, and the theory involving nonlocal terms is often not well understood. Emphasis is placed in mathematical biology, a growing field in which many new models have appeared in recent years. The main motivation of this workshop is tobring together researchers working in this area to promote discussion of ideas which can be useful across several models, developing the relevant mathematical framework.
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Les modèles mathématiques basés sur des équations aux dérivées partielles sont omniprésents dans la compréhension des phénomènes naturels, et la biologie ne fait pas exception. Il s’avère que de nombreux modèles phénoménologiques en biologie nécessitent, ou bénéficient de l’introduction de termes non locaux qui impliquent le comportement de la fonction de distribution en plusieurs points, par opposition aux termes locaux plus courants impliquant des dérivées. Plusieurs exemples pertinents en biologie concernent la vitesse de propagation des espèces en écologie, les modèles de sélection-mutation en biologie évolutive (dans le contexte du changement climatique, par exemple), les processus de croissance-fragmentation pertinents pour les cellules et les agrégats, les modèles de population neuronale, les questions de ségrégation de populations en écologie et biologie, etc. Ces modèles partagent des difficultés mathématiquessimilaires et la théorie impliquant des termes non locaux n’est souvent pas bien comprise. L’accent est mis sur la biologie mathématique, un domaine en pleine croissance dans lequel de nombreux nouveaux modèles sont apparus ces dernières années. La principale motivation de cette conférence est de rassembler des chercheurs travaillant dans ce domaine afin de promouvoir l’échange d’idées pouvant être utiles pour plusieurs modèles, dans le but de développer ainsi un cadre mathématique pertinent.
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Alexis Leculier (Université Toulouse III) Analysis of two « Rolling carpet » strategies to repulse an invasion
Vincent Calvez (Université Claude Bernard Lyon 1) Mathematical modeling of cell collective motion triggered by self-generated gradients
Cécile Carrère (Université d’Orléans) Influence of mutations in phenotypically structured populations in a time periodic environment
Jérôme Coville (INRA Avignon) Propagation phenomena in homogeneous non local monostable equation: What’s new ?
Pierre Degond (Imperial College London) Body orientation dynamics
Léonard Dekens (Université Claude Bernard Lyon 1) Sexual reproduction and spatial heterogeneities:
an asymptotic analysis on the evolutionary dynamics of complex traits
Laurent Desvillettes (Université de Paris) About a parabolic system (involving chemotaxis) coming out of the modeling of autoimmune diseases
Arnaud Ducrot (Université Le Havre Normandie) Threshold effects for a one-dimensional bistable equation with nonlocal diffusion
Quentin Griette (Université de Bordeaux) On the competitive exclusion principle for continuously distributed populations
Piotr Gwiazda (Polish Academy of Sciences) Spaces of Measures and their Applications to Structured Population Models
François Hamel (Aix-Marseille Université) Persistence and extinction for nonlocal reaction-diffusion equations with Allee threshold
Thomas Lepoutre (Université Claude Bernard Lyon 1) Nonlocal model of cell-cell interaction modelling yeast polarization
Hugo Martin (Sorbonne Université) Periodic asymptotic dynamics of the measure solutions to a growth-fragmentation equation in a critical case
Sara Merino-Aceituno (University of Vienna) Nematic alignment of self-propelled particles in the macroscopic regime
Nicolas Meunier (Université de Paris) Mathematical analysis and numerical simulations on models of cell motility
Gwenaël Peltier (Université de Montpellier) Population facing a nonlinear environmental gradient: a perturbation approach
Benoît Perthame (Sorbonne Université) Structured equations in biology
David Poyato (Université Lyon 1) Long-term behavior of a time-discrete sexual reproduction model under the effect of selection
Gael Raoul (Ecole Polytechnique) Dynamics of a kinetic model from evolutionary biology
Anaïs Rat (Aix-Marseille Université) Growth-fragmentation model for a size-structured population presenting heterogeneity
in growth rate: Malthus parameter and long-time behavior
Michèle Romanos (Université Toulouse III) A multi-tissue viscous model for tissue growth: incompressible limitand qualitative
behaviour at the Hele-Shaw limit
Lionel Roques (INRA Avignon) Surviving when the phenotypic optimum changes: a PDE approach
Zuzanna Szymanska (University of Warsaw) Bayesian inference of a non-local proliferation model
Milica Tomasevic (Ecole Polytechnique) On a multi-type growth-fragmentation process modelling the mycelial network of a filamentous fungus
Lara Trussardi (University of Vienna) Nonlocal-to-local convergence of Cahn-Hilliard equations
Havva Yoldas (Université Lyon 1) Long-time behaviour of the run and tumble equation
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