Related papers: Speed and shape of population fronts with density-…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
Fitness consequence of dispersal depends on property of the entire landscape, which patches are available and what are the cost of moving. These are information that are not available locally when an organism make the decision to disperse.…
We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche. This model consists of a system of coupled…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
We study flow-induced enhancement of the speed of pulsating traveling fronts for reaction-diffusion equations, and quenching of reaction by fluid flows. We prove, for periodic flows in two dimensions and any combustion-type reaction, that…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
Starting from an age-structured diffusive population growth law for single species in a discrete and periodic habitat, we formulate a stage structured population model with spatially periodic dispersal, mortality and recruitment. With a KPP…
We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is…
This study builds upon a model proposed by Joanny and collaborators that examines the dynamics of interfaces between two distinct cell populations, particularly during tumor growth in healthy tissues. This framework leads to the…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape…
Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the…
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
We consider a model of individual clustering with two specific reproduction rates and small diffusion parameter in one space dimension. It consists of a drift-diffusion equation for the population density coupled to an elliptic equation for…