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The purpose of this paper is to investigate the principal spectral theory and asymptotic behavior of the spectral bound for cooperative nonlocal dispersal systems, specifically focusing on the case where partial diffusion coefficients are…
This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal rates. We first deal…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
This paper is devoted to the study of asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficients. We first establish the continuity of the basic…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
It is well known that, in the study of the dynamical properties of nonlinear evolution system with nonlocal dispersals, the principal eigenvalue of linearized system play an important role. However, due to lack of compactness, in order to…
The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the…
The principal eigenvalue for linear elliptic operator has been known to be one of very useful tools to investigate many important partial differential equations. Due to the pioneering works of Berestycki et al. \cite{BCV1,BCV2}, the study…
In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…
Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other…
This paper is to investigate the dependence of the principal spectrum points of nonlocal dispersal operators on underlying parameters and to consider its applications. In particular, we study the effects of the spatial inhomogeneity, the…
In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…
In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number $R_0$ and show that $R_0$ is a threshold parameter: if $R_0\le 1$ the disease free steady state is globally stable; if $R_0>1$…
We study a nonlocal SIS epidemic model with free boundaries, advection, and spatial heterogeneity, where the dispersal kernels are not assumed to be symmetric. The model describes the evolution of susceptible and infected populations in a…
In this paper, we study the spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions subject to Dirichlet type, Neumann type and spatial periodic type boundary conditions. We first obtain necessary and…
To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal SIS (susceptible-infected-susceptible)…
In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long…
This paper investigates the principal spectral theory and the asymptotic behavior of the principal spectrum point for a class of time-periodic cooperative systems with nonlocal dispersal operators, incorporating both coupled and uncoupled…
We study the Suscectible-Infected-Recovered-Susceptible (SIRS) epidemic model on deterministic networks. For connected but otherwise general interaction patterns and heterogeneous recovery and loss-of-immunity rates, we identify a…
In this paper we put forward a viral propagation model with nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential…