A5023210540- Mathematical and Theoretical Epidemiology and Ecology Models
- Nonlinear Differential Equations Analysis
- Evolution and Genetic Dynamics
- Nonlinear Partial Differential Equations
- Advanced Mathematical Modeling in Engineering
- Differential Equations and Boundary Problems
- Mathematical Biology Tumor Growth
- Fractional Differential Equations Solutions
- Differential Equations and Numerical Methods
- Spectral Theory in Mathematical Physics
- Advanced Mathematical Physics Problems
- Plant Virus Research Studies
- advanced mathematical theories
- Stability and Controllability of Differential Equations
- Nonlinear Dynamics and Pattern Formation
- Stochastic processes and statistical mechanics
- Numerical methods in inverse problems
- Evolutionary Game Theory and Cooperation
- Plant and Fungal Interactions Research
- Bioenergy crop production and management
- Phytoplasmas and Hemiptera pathogens
- Plant Disease Resistance and Genetics
- Wheat and Barley Genetics and Pathology
- Genetic Mapping and Diversity in Plants and Animals
- Safety and Risk Management
Biostatistique et Processus Spatiaux
2016-2025
Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement
2020-2024
institut Camille-Jordan
2024
Centre National de la Recherche Scientifique
2024
Université Jean Monnet
2024
École Centrale de Lyon
2024
Institut National des Sciences Appliquées de Lyon
2024
Université Claude Bernard Lyon 1
2024
Weatherford College
2021
Universidad Nacional de Colombia
2021
We study a one-dimensional non-local variant of Fisher's equation describing the spatial spread mutant in given population, and its generalization to so-called monostable nonlinearity. The dispersion genetic characters is assumed follow diffusion law modelled by convolution operator. prove that, as classical (local) problem, there exist travelling-wave solutions arbitrary speed beyond critical value also characterize asymptotic behaviour such at infinity. Our proofs rely on an appropriate...
We consider a nonlocal reaction-diffusion equation as model for population structured by space variable and phenotypic trait. To sustain the possibility of invasion in case where an underlying principal eigenvalue is negative, we investigate existence travelling wave solutions. identify minimal speed c* > 0, prove waves when c ≥ nonexistence 0 ≤ < c*.
We aim at saying as much possible about the spectra of three classes linear diffusion operators involving nonlocal terms. In all but one cases, we characterize minimum $λ_p$ real part spectrum in two max-min fashions, and prove that most cases is an eigenvalue with a corresponding positive eigenfunction, algebraically simple isolated; also maximum principle holds if only $λ_p>0$ (in cases) or $≥ 0$ case). these results by elementary method based on strong principle, rather than resorting to...
Let $J \in C(\mathbb{R})$, $J\ge 0$, $\int_{\tiny$\mathbb{R}$} J = 1$ and consider the nonlocal diffusion operator $\mathcal{M}[u] \star u - u$. We study equation $\mathcal{M} + f(x,u) $u \ge in $\mathbb{R}$, where $f$ is a KPP-type nonlinearity, periodic $x$. show that principal eigenvalue of linearization around zero well defined nontrivial solution nonlinear problem exists if only this negative. prove if, additionally, $J$ symmetric, then unique.
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is provide a unified proof in very broad framework using simple real analysis tools. particular, review results that already exist literature and complete table. It appears most important case bistable nonlinearity, which then extend other classical nonlinearities.
Uncovering how natural selection and genetic drift shape the evolutionary dynamics of virus populations within their hosts can pave way to a better understanding emergence. Mathematical models already play leading role in these studies are intended predict future emergences. Here, using high-throughput sequencing, we analyzed within-host population four Potato Y (PVY) variants differing at most by two substitutions involved pathogenicity properties. Model procedures were used compare...
In this paper, we analyse the structure of set positive solutions an heterogeneous nonlocal equation form: $$ \int_{\Omega} K(x, y)u(y)\,dy -\int_ {\Omega}K(y, x)u(x)\, dy + a_0u+\lambda a_1(x)u -\beta(x)u^p=0 \quad \text{in}\quad \Omega$$ where $\Omega\subset \mathbb{R}^n$ is a bounded domain, $K\in C(\mathbb{R}^n\times \mathbb{R}^n) $ non-negative, $a_i,\beta \in C(\Omega)$ and $\lambda\in\mathbb{R}$. Such type appears in some studies population dynamics evolves partially controlled...
We are concerned with travelling wave solutionsarising in a reaction diffusion equation bistable andnonlocal nonlinearity, for which the comparison principle does nothold. Stability of equilibrium $u\equiv 1$ is not assumed. Weconstruct solution connecting 0 to an unknownsteady state, 'above and away', from theintermediate equilibrium. For focusing kernels we prove that, asexpected, connects 1. Our results also apply readilyto nonlocal ignition case.