Related papers: Uniqueness result for an age-dependent reaction-di…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We establish H\"older regularity for the weak solution to a degenerate diffusion equation in the presence of a local (drift) potential and nonlocal (interaction) term, posed in a bounded domain with no-flux boundary conditions. The…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…
We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density dependent fecundity regulation mechanism. We establish existence and uniqueness of this process and…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…
We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and…
We show that for a family of problems described by non-linear diffusion equations an exact calculation of the two time correlation function gives C(t,t')=f(t-t')g(t'), t>t', exhibiting normal and anomalous diffusions, as well as aging…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
In this paper, we investigate an eigenvalue problem associated with an age-structured operator incorporating random diffusion and advection. Our primary focus is on examining the asymptotic behaviors of the principal eigenvalue with respect…
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…
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…