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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 pathogens: the wild type and the mutant. The system is of a…

Analysis of PDEs · Mathematics 2025-01-22 Quentin Griette , Hiroshi Matano

An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…

Analysis of PDEs · Mathematics 2024-05-08 Lei Li , Mingxin Wang

We investigate the phenomenology emerging from a 2-species dynamics under the scenario of a quasi-neutral competition within a metapopulation framework. We employ stochastic and deterministic approaches, namely spatially-constrained…

Populations and Evolution · Quantitative Biology 2021-02-05 Marcelo A. Pires , Nuno Crokidakis , Silvio M. Duarte Queirós

We consider a one-dimensional free boundary problem describing the migration of diffusants into rubber. In our setting, the free boundary represents the position of the front delimitating the diffusant region. The growth rate of this region…

Analysis of PDEs · Mathematics 2022-01-06 Kota Kumazaki , Toyohiko Aiki , Adrian Muntean

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer…

Populations and Evolution · Quantitative Biology 2023-09-14 Elliott Hughes , Miguel Moyers-Gonzalez , Rua Murray , Phillip L. Wilson

The current paper is to investigate the numerical approximation of logistic type chemotaxis models in one space dimension with a free boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject…

Numerical Analysis · Mathematics 2019-07-16 Lei Yang , Lianzhang Bao

Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion…

Other Condensed Matter · Physics 2011-10-28 O. A. Dvoretskaya , P. S. Kondratenko

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive…

Populations and Evolution · Quantitative Biology 2015-12-16 Sebastian J. Schreiber , Timothy P. Killingback

This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate…

Analysis of PDEs · Mathematics 2026-04-17 Wen Tao , Wan-Tong Li , Shigui Ruan , Wen-Bing Xu

Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity…

Populations and Evolution · Quantitative Biology 2023-04-14 Ami Taitelbaum , Robert West , Mauro Mobilia , Michael Assaf

The entanglement of population dynamics, evolution, and adaptive radiation for species competing for resources is studied. For resource harvesting, we modify the model used in Ref. Phys. Rev. Lett. 118 048103 and introduce new resource…

Populations and Evolution · Quantitative Biology 2023-10-03 Sergei V. Koniakhin

In many natural situations one observes a local system with many competing species which is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When…

Populations and Evolution · Quantitative Biology 2017-07-26 Yael Fried , Nadav M. Shnerb , David A. Kessler

Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…

Statistical Mechanics · Physics 2020-07-14 Ching-Hao Wang , Sakib Matin , Ashish B. George , Kirill S. Korolev

We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…

Chaotic Dynamics · Physics 2015-05-20 John Grant , Michael Wilkinson

This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann…

Analysis of PDEs · Mathematics 2022-11-08 Mingxin Wang

Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended…

Populations and Evolution · Quantitative Biology 2015-03-17 Daniel Groselj , Frank Jenko , Erwin Frey

In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…

Dynamical Systems · Mathematics 2017-12-22 Ruiwen Wu , Xiao-Qiang Zhao

We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…

Analysis of PDEs · Mathematics 2020-02-26 Emeric Bouin , Guillaume Legendre , Yuan Lou , Nichole Slover

Competition between languages or cultural traits diffusing in the same geographical area is studied combining the language competition model of Abrams and Strogatz and a human dispersal model on an inhomogeneous substrate. Also, the effect…

Physics and Society · Physics 2009-11-13 Marco Patriarca , Els Heinsalu

We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…

Analysis of PDEs · Mathematics 2022-12-06 Henri Berestycki , Alessandro Zilio