Related papers: Selected topics on reaction-diffusion-advection mo…
We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical…
How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions…
In this paper, we investigate a Lotka-Volterra competition-diffusion system with self-memory effects and spatial heterogeneity under Dirichlet boundary conditions. We focus on how memory strength influences the coexistence and stability of…
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…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
Phenotypic heterogeneity is a strategy commonly used by bacteria to rapidly adapt to changing environmental conditions. Here, we study the interplay between phenotypic heterogeneity and genetic diversity in spatially extended populations.…
A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary…
Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of…
Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
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…
We investigate the long term behavior for a class of competition-diffusion systems of Lotka-Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We study the impact of contact heterogeneity on epidemic dynamics. A system characterized by multiple susceptible populations is considered. The description of the spread of an infectious disease is obtained through the study of a system of…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak-Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
We investigate the competing effects and relative importance of intrinsic demographic and environmental variability on the evolutionary dynamics of a stochastic two-species Lotka-Volterra model by means of Monte Carlo simulations on a…