相关论文: Nonlocal diffusion and pulse intervention in a fae…
We consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a L\'evy process and can reach resources in a…
The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible-Infectious-Recovered (SIR) model applicable across a wide range of basic reproduction numbers $R_o$. The focus is on the…
Spatial heterogeneity and habitat characteristic are shown to determine the asymptotic profile of the solution to a reaction-diffusion model with free boundary, which describes the moving front of the invasive species. A threshold value…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…
We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…
This paper shows the global existence and boundedness of solutions of a reaction diffusion system modeling liver infections. The existence proof is presented step by step and the focus lies on the interpretation of intermediate results in…
We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a…
Reaction-diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many models of biological invasion are extensions of the…
We study a stochastic spatial epidemic model where the $N$ individuals carry two features: a position and an infection state, interact and move in $\R^d$. In this Markovian model, the evolution of the infection states are described with the…
Bootstrap percolation is an often used model to study the spread of diseases, rumors, and information on sparse random graphs. The percolation process demonstrates a critical value such that the graph is either almost completely affected or…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form $SI$, and study the spatial profile of population distribution as the movement rate of the infected individuals…
Interaction patterns among individuals play vital roles in spreading infectious diseases. Understanding these patterns and integrating their impact in modeling diffusion dynamics of infectious diseases are important for epidemiological…
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the…
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…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…