79 citations · 127 across the 25 of their papers we have counts for
26 papers
On measure-valued solutions for a structured population model with transfers
Pierre Magal, Gaël Raoul
We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to popula…
Population dynamics model for aging
Jacques Demongeot, Pierre Magal
The chronological age used in demography describes the linear evolution of the life of a living being. The chronological age cannot give precise information about the exact develop…
Data-Driven Mathematical Modeling Approaches for COVID-19: a survey
J. Demongeot, P. Magal
In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of gr…
Forecasting the changes between endemic and epidemic phases of a contagious disease, with the example of COVID-19
Jacques Demongeot, Pierre Magal, Kayode Oshnubi
Predicting the endemic/epidemic transition during the temporal evolution of a contagious disease. Methods: Defining indicators for detecting the transition endemic/epidemic, with f…
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…
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…
Return-to-home model for short-range human travel
Arnaud Ducrot, Pierre Magal
In this work, we develop a mathematical model to describe the local movement of individuals by taking into account their return to home after a period of travel. We provide a suita…
An integrated semigroup approach for age structured equations with diffusion and non-homogeneous boundary conditions
Arnaud Ducrot, Pierre Magal, Alexandre Thorel
In this work, we consider a linear age-structured problem with diffusion and non-homogeneous boundary conditions both for the age and the space variables. We handle this linear pro…
A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model
Arnaud Ducrot, Hao Kang, Pierre Magal
In this paper, we provide a short proof for the Hopf bifurcation theorem in the Gurtin-MacCamy's population dynamics model. Here we use the Crandall and Rabinowitz's approach, base…
Global asymptotic stability for Gurtin-MacCamy's population dynamics model
Zhaohai Ma, Pierre Magal
In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker's type of birth function. This model is a hyperbolic part…
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 Holling's predator-prey model with handling and searching predators
Sze-Bi Hsu, Zhihua Liu, Pierre Magal
The goal of this paper is to explain how to derive the classical Rosenzweig-MacArthur's model by using a model with two groups of predators in which we can separate the vital dynam…
Large Speed Traveling Waves for the Rosenzweig-MacArthur Model with Spatial Diffusion
Arnaud Ducrot, Zhihua Liu, Pierre Magal
This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence a…
Positively Invariant Subset for Non-Densely Defined Cauchy Problems
Pierre Magal, Ousmane Seydi
In this article we prove the positive invariance of a closed subset by the semiflow generated by a semi-linear non densely Cauchy problem. The condition impose to obtain such a pro…
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…
Monotone abstract non-densely defined Cauchy problems applied to age structured population dynamic models
Pierre Magal, Ousmane Seydi, Feng-Bin Wang
In this article we first derive some sufficient conditions to establish the monotonicity and comparison principles of the semi-flow generated by non-densely defined Cauchy problems…
Asymptotic behavior of a nonlocal advection system with two populations
Xiaoming Fu, Pierre Magal
In this paper, we consider a nonlocal advection model for two populations on a bounded domain. The first part of the paper is devoted to the existence and uniqueness of solutions a…
Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions
Zhihua Liu, Pierre Magal
In this article we study a class of delay differential equations with infinite delay in weighted spaces of uniformly continuous functions. We focus on the integrated semigroup form…
On a Vector-host Epidemic Model with Spatial Structure
Pierre Magal, G. F. Webb, Yixiang Wu
In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number and show that is a threshold parameter: if t…
Spatial Spread of Epidemic Diseases in Geographical Settings: Seasonal Influenza Epidemics in Puerto Rico
Pierre Magal, Glenn F. Webb, Yixiang Wu
Deterministic models are developed for the spatial spread of epidemic diseases in geographical settings. The models are focused on outbreaks that arise from a small number of infec…
A system of state-dependent delay differential equation modelling forest growth I: semiflow properties
Pierre Magal, Zhengyang Zhang
In this article we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the n…
A system of state-dependent delay differential equation modelling forest growth II: boundedness of solutions
Pierre Magal, Zhengyang Zhang
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundednes…
Variation of constants formula and exponential dichotomy for non autonomous non densely defined Cauchy problems
Pierre Magal, Ousmane Seydi
In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-…
Dynamics of a kinetic model describing protein exchanges in a cell population
Pierre Magal, Gaël Raoul
We consider a cell population structured by a positive real number, describing the number of P-glycoproteins carried by the cell. We are interested in the effect of those proteins…