相关论文: Nonlocal Diffusion Elliptic System Modelling The B…
In this paper, we give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system.
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection…
In this paper, we study a nonlocal evolution system. We apply abstract results from the bifurcation theory to obtain the existence of coexistence states. Their stability are investigated as well.
To explore the coupling between a growing population of microorganisms such as E. coli and a nonuniform nutrient distribution, we formulate a minimalistic model. It consists of active Brownian particles that divide and grow at a…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…
The transition from localized to systemic spreading of bacteria, viruses and other agents is a fundamental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple…
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-\Delta)^{s_i}u_i$…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
Following \cite{ipel1}, we consider a nonlinear SIS-type nonlocal system describing the spread of epidemics on networks, assuming nonlimited transmission, We prove local existence of a unique solution for any diffusion coefficients and…
This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links…
In this paper we study a mathematical model for an infectious disease such as Cholera without life-time immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are…
In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
The revival mechanism in dormant bacteria is a puzzling and open issue. We propose a model of information diffusion on a regular grid where agents represent bacteria and their mutual interactions implement quorum sensing. Agents may have…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
In this work, we consider a reaction-diffusion system, modeling the interaction between nutrients, phytoplanktons and zooplanktons. Using a semigroup approach in $L^2$, we prove global existence, uniqueness and positivity of the solutions.…