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Mesoscopic models for propagation in biology

Total Cost €


EC-Contrib. €






 MESOPROBIO project word cloud

Explore the words cloud of the MESOPROBIO project. It provides you a very rough idea of what is the project "MESOPROBIO" about.

scales    age    waves    analogy    kinetic    anomalous    separate    local    competition    approximation    evolutionary    history    intermediate    biologists    bacteria    hyperbolic    description    mesoscale    parabolic    jacobi    phenotypical    theory    dispersal    lyon    placed    hamilton    refers    models    structured    interaction    collaborations    geometric    austria    outcomes    possibly    maximum    quantitative    feedback    structure    gases    according    scattering    reaction    mathematical    lacking    optimal    individual    foraging    macroscale    optics    nonlocal    directions    respect    hub    equations    heterogeneity    questions    pde    microscale    basic    interplay    complexity    traits    arguments    close    biology    diffusion    uk    phenomena    track    fronts    answer    push    trait    mesoprobio    arising    space    appropriate    concentration    life    transport    populations    strategies    dynamics    accelerating    propagation    upscaling    velocity    travelling    biological    emphasis    sciences    french    multiscale    cope   

Project "MESOPROBIO" data sheet

The following table provides information about the project.


Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙091˙688 €
 EC max contribution 1˙091˙688 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2020-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

According to biologists, there is a need for quantitative models that are able to cope with the complexity of problems arising in the field of life sciences. Here, complexity refers to the interplay between various scales that are not clearly separate. The great challenge of the MESOPROBIO project is to analyse complex PDE models for biological propagation phenomena at the mesoscale. By analogy with the kinetic theory of gases, this is an intermediate level of description between the microscale (individual-based models) and the macroscale (parabolic reaction-transport-diffusion equations). The specific feature common to all the models involved in the project is the local heterogeneity with respect to a structure variable (velocity, phenotypical trait, age) which requires new mathematical methods. I propose to push analysis beyond classical upscaling arguments and to track the local heterogeneity all along the analysis.

The biological applications are: concentration waves of bacteria, evolutionary aspects of structured populations (with respect to dispersal ability or life-history traits), and anomalous diffusion. The mathematical challenges are: multiscale analysis of PDE having different properties in different directions of the phase space, including nonlocal terms (scattering, competition), and possibly lacking basic features of reaction-diffusion equations such as the maximum principle. The outcomes are: travelling waves, accelerating fronts, approximation of geometric optics, nonlocal Hamilton-Jacobi equations, optimal foraging strategies and evolutionary dynamics of phenotypical traits. Emphasis will be placed on quantitative results with strong feedback towards biology.

The project will be conducted in Lyon, a French hub for mathematical biology and hyperbolic equations. There will be close interaction with biologists in order to establish the most appropriate questions to answer. Several collaborations in Europe (UK, Austria) will be developed.


year authors and title journal last update
List of publications.
Spreading in kinetic reaction–transport equations in higher velocity dimensions
published pages: 1-29, ISSN: 0956-7925, DOI: 10.1017/S0956792518000037
European Journal of Applied Mathematics 2019-05-29
2017 Sylvain Gandon, Sepideh Mirrahimi
A Hamilton–Jacobi method to describe the evolutionary equilibria in heterogeneous environments and with non-vanishing effects of mutations
published pages: 155-160, ISSN: 1631-073X, DOI: 10.1016/j.crma.2016.12.001
Comptes Rendus Mathematique 355/2 2019-05-29
2017 Vincent Calvez, Laurent Gosse, Monika Twarogowska
Travelling Chemotactic Aggregates at Mesoscopic Scale and BiStability
published pages: 2224-2249, ISSN: 0036-1399, DOI: 10.1137/16M1108108
SIAM Journal on Applied Mathematics 77/6 2019-05-29
2017 Nils Caillerie
Large deviations of a velocity jump process with a Hamilton–Jacobi approach
published pages: 170-175, ISSN: 1631-073X, DOI: 10.1016/j.crma.2016.12.011
Comptes Rendus Mathematique 355/2 2019-05-29
2017 Emeric Bouin, Christopher Henderson, Lenya Ryzhik
The Bramson logarithmic delay in the cane toads equations
published pages: 599-634, ISSN: 0033-569X, DOI: 10.1090/qam/1470
Quarterly of Applied Mathematics 75/4 2019-05-29
2016 Hugues Berry, Thomas Lepoutre, Álvaro Mateos González
Quantitative Convergence Towards a Self-Similar Profile in an Age-Structured Renewal Equation for Subdiffusion
published pages: 15-45, ISSN: 0167-8019, DOI: 10.1007/s10440-016-0048-3
Acta Applicandae Mathematicae 145/1 2019-05-29
2017 Emeric Bouin, Christopher Henderson
Super-linear spreading in local bistable cane toads equations
published pages: 1356-1375, ISSN: 0951-7715, DOI: 10.1088/1361-6544/aa5d65
Nonlinearity 30/4 2019-05-29
2018 Vincent Calvez, Benoȋt Perthame, Shugo Yasuda
Traveling wave and aggregation in a flux-limited Keller-Segel model
published pages: 891-909, ISSN: 1937-5077, DOI: 10.3934/krm.2018035
Kinetic & Related Models 11/4 2019-05-29
2017 Vincent Calvez, Thomas O. Gallouët
Blow-Up Phenomena for Gradient Flows of Discrete Homogeneous Functionals
published pages: , ISSN: 0095-4616, DOI: 10.1007/s00245-017-9443-z
Applied Mathematics & Optimization 2019-05-29
2017 Vincent Calvez, José Antonio Carrillo, Franca Hoffmann
The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime
published pages: 1-71, ISSN: , DOI: 10.1007/978-3-319-61494-6_1
Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions 2019-04-18
2017 Lionel Roques, Jimmy Garnier, Guillaume Martin
Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach
published pages: , ISSN: 2045-2322, DOI: 10.1038/s41598-017-17212-5
Scientific Reports 7/1 2019-04-18
2017 Thibault Bourgeron, Vincent Calvez, Jimmy Garnier, Thomas Lepoutre
Existence of recombination-selection equilibria for sexual populations
published pages: , ISSN: , DOI:
2017 Vincent Calvez, Laurent Gosse, Monika Twarogowska
Concentration Waves of Chemotactic Bacteria: The Discrete Velocity Case
published pages: 79-109, ISSN: , DOI: 10.1007/978-3-319-49262-9_3
Innovative Algorithms and Analysis 2019-04-18
2018 Emeric Bouin, Jimmy Garnier, Christopher Henderson, Florian Patout
Thin Front Limit of an Integro-differential Fisher-KPP Equation with Fat-Tailed Kernels
published pages: 3365-3394, ISSN: 0036-1410, DOI: 10.1137/17M1132501
SIAM Journal on Mathematical Analysis 50/3 2019-04-18
2018 Mirrahimi , Sepideh
Singular limits for models of selection and mutations with heavy-tailed mutation distribution
published pages: , ISSN: , DOI: 2019-04-18
2016 Vincent Calvez
Chemotactic waves of bacteria at the mesoscale
published pages: , ISSN: , DOI:
2017 Sepideh Mirrahimi
A Hamilton–Jacobi approach to characterize the evolutionary equilibria in heterogeneous environments
published pages: 2425-2460, ISSN: 0218-2025, DOI: 10.1142/S0218202517500488
Mathematical Models and Methods in Applied Sciences 27/13 2019-04-18
2018 Bouin , Emeric; Chan , Matthew H.; Henderson , Christopher; Kim , Peter S.
Influence of a mortality trade-off on the spreading rate of cane toads fronts
published pages: , ISSN: , DOI:
2017 2019-04-18
2018 FIGUEROA IGLESIAS , Susely; Mirrahimi , Sepideh
Long time evolutionary dynamics of phenotypically structured populations in time periodic environments
published pages: , ISSN: , DOI: 2 2019-04-18
2018 Hélène Hivert
A first-order asymptotic preserving scheme for front propagation in a one-dimensional kinetic reaction–transport equation
published pages: 253-278, ISSN: 0021-9991, DOI: 10.1016/
Journal of Computational Physics 367 2019-04-18

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