33 citations · 101 across the 24 of their papers we have counts for
26 papers
Heteroclinic cycles and long-time behavior in a singularly perturbed three-species Lotka--Volterra system
Arnaud Ducrot, Quentin Griette, Quang-Vinh Tran
We study a three-species competitive Lotka--Volterra system with cyclic dominance, motivated by rock--paper--scissors interactions in ecological communities. The model contains a s…
Bistable wavefronts in the Gurtin-MacCamy population model
Quentin Griette, Franco Herrera, Hao Kang
In this paper we prove the existence of monotone traveling wave solutions for an age-structured population model with a monotone and bistable nonlinearity. We formulate the problem…
Propagation dynamics of an acid-mediated invasion model with degenerate tumor diffusion
Xinyue Cao, Quentin Griette, Xiong Li +1
We investigate traveling wave fronts for an acid-mediated tumor invasion model with density-dependent degenerate diffusion. The model is a partially diffusive PDE--ODE system of Ga…
Propagation phenomena in KPP-bistable periodic patchy environments
Quentin Griette, François Hamel, Mingmin Zhang +1
This paper first investigates the propagation dynamics of solutions to the Cauchy problem for a one-dimensional reaction-diffusion equation in a spatially periodic environment cons…
On advective nonlocal operators: multiplicity of principal eigenpairs
Arnaud Ducrot, Quentin Griette, Xing Liang
We study the existence and multiplicity of principal eigenvalues and eigenfunctions for a periodically heterogeneous nonlocal dispersal model with advection. The operator we consid…
Front propagation in hybrid reaction-diffusion epidemic models with spatial heterogeneity. Part II: Pulsating traveling waves
Quentin Griette, Hiroshi Matano
We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of patho…
Sharp threshold dynamics for a bistable age-structured population model
Quentin Griette, Franco Herrera
This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of i…
Slowly oscillating periodic solutions in a nonlinear Volterra equation with non-symmetric feedback
Quentin Griette, Franco Herrera
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particul…
Front propagation into unstable states for periodic monotone reaction-diffusion systems
Liangliang Deng, Arnaud Ducrot, Quentin Griette
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that con…
Front propagation in hybrid reaction-diffusion epidemic models with spatial heterogeneity. Part I: Spreading speed and asymptotic behavior
Quentin Griette, Hiroshi Matano
We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of patho…
Robin Hood model versus Sheriff of Nottingham model: transfers in population dynamics
Quentin Griette, Pierre Magal
We study the problem of transfers in a population structured by a continuous variable corresponding to the quantity being transferred. The model takes the form of an integro-differ…
Asymptotic behavior of an epidemic model with infinitely many variants
Jean-Baptiste Burie, Arnaud Ducrot, Quentin Griette
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction nu…
Speed-up of traveling waves by negative chemotaxis
Quentin Griette, Christopher Henderson, Olga Turanova
We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of repulsive chemotaxis and provide an almost complete picture of its asymptotic dependence on…
A Kermack-McKendrick model with age of infection starting from a single or multiple cohorts of infected patients
Jacques Demongeot, Quentin Griette, Yvon Maday +1
During an epidemic, the infectiousness of infected individuals is known to depend on the time since the individual was infected, that is called the age of infection. Here we study…
Traveling waves with continuous profile for hyperbolic Keller-Segel equation
Quentin Griette, Pierre Magal, Min Zhao
This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion. We ass…
Propagation dynamics of solutions to spatially periodic reaction-diffusion systems with hybrid nonlinearity
Quentin Griette, Hiroshi Matano
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly…
Epidemic models in measure spaces: persistence, concentration and oscillations
Jean-Baptiste Burie, Arnaud Ducrot, Quentin Griette
We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structure…
The spatio-temporal dynamics of interacting genetic incompatibilities. Part I: The case of stacked underdominant clines
Matthieu Alfaro, Quentin Griette, Denis Roze +1
We explore the interaction between two genetic incompatibilities (underdominant loci in diploid organisms) in a population occupying a one-dimensional space. We derive a system of…
Sharp discontinuous traveling waves in a hyperbolic Keller--Segel equation
Xiaoming Fu, Quentin Griette, Pierre Magal
In this work we describe a hyperbolic model with cell-cell repulsion with a dynamics in the population of cells. More precisely, we consider a population of cells producing a field…
A Liouville-type result for non-cooperative Fisher--KPP systems and nonlocal equations in cylinders
Léo Girardin, Quentin Griette
We address the uniqueness of the nonzero stationary state for a reaction-diffusion system of Fisher-KPP type that does not satisfy the comparison principle. Although the uniqueness…
Concentration estimates in a multi-host epidemiological model structured by phenotypic traits
Jean-Baptiste Burie, Arnaud Ducrot, Quentin Griette +1
In this work we consider an epidemic system modelling the evolution of a spore-producing pathogen within a multi-host population of plants. Here we focus our analysis on the study…
A cell-cell repulsion model on a hyperbolic Keller-Segel equation
Xiaoming Fu, Quentin Griette, Pierre Magal
In this work, we discuss a cell-cell repulsion population dynamic model based on a hyperbolic Keller-Segel equation with two populations. This model can well describe the cell grow…
Kinetic equations and self-organized band formations
Quentin Griette, Sebastien Motsch
Self-organization is an ubiquitous phenomenon in nature which can be observed in a variety of different contexts and scales, with examples ranging from fish schools, swarms of bird…
Singular measure traveling waves in an epidemiological model with continuous phenotypes
Quentin Griette
We consider the reaction-diffusion equation \begin{equation*} u_t=u_{xx}+μ\left(\int_ΩM(y,z)u(t,x,z)dz-u\right) + u\left(a(y)-\int_ΩK(y,z) u(t,x,z)dz\right) , \end{equation*} where…