A nonlocal dispersal logistic equation with spatial degeneracy

Sun, Jian-Wen; Li, Wan–Tong; Wang, Zhicheng

doi:10.3934/dcds.2015.35.3217

Cited by 39 publications

(20 citation statements)

References 42 publications

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“…Equations of form (1.1) have been used to model different diffusion phenomena in the literature and attracted considerable interests, for example, the papers [3][4][5][6][7][8]. Equations of form (1.1) have been used to model different diffusion phenomena in the literature and attracted considerable interests, for example, the papers [3][4][5][6][7][8].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Asymptotic behavior for non-homogeneous nonlocal dispersal equations

Sun

2015

Applied Mathematics Letters

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Asymptotic behavior for non-homogeneous nonlocal dispersal equations

Sun

2015

Applied Mathematics Letters

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“…Likewise when nonlocal terms are incorporated into models, studying the spectrum of the linearized problem is also an important step and the corresponding results have wide applications. For example, Turing patterns driven by nonlocal diffusion are studied in [4], single species model and competition systems with nonlocal dispersal are investigated in [1,2,5,9,16,21,22], and in [20,23], logistic equations with nonlocal interaction are considered.…”

Section: Fang LI Jerome Coville and Xuefeng Wangmentioning

confidence: 99%

On eigenvalue problems arising from nonlocal diffusion models

Li¹,

Coville

Wang³

2017

Discrete &Amp; Continuous Dynamical Systems - A

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We aim at saying as much as possible about the spectra of three classes of linear diffusion operators involving nonlocal terms. In all but one cases, we characterize the minimum λp of the real part of the spectrum in two max-min fashions, and prove that in most cases λp is an eigenvalue with a corresponding positive eigenfunction, and is algebraically simple and isolated; we also prove that the maximum principle holds if and only if λp > 0 (in most cases) or ≥ 0 (in one case). We prove these results by an elementary method based on the strong maximum principle, rather than resorting to Krein-Rutman theory as did in the previous papers. In one case when it is impossible to characterize λp in the max-min fashion, we supply a complete description of the whole spectrum.

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“…Then, we have the following result. The proof of Lemma 4.2 can be found in [5,8,25]. We omit it here.…”

Section: The Endemic Equilibriummentioning

confidence: 99%

Dynamics of a nonlocal dispersal SIS epidemic model

Yang¹,

Li²

2017

Communications on Pure &Amp; Applied Analysis

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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 introduce a basic reproduction number R 0 and establish threshold-type results on the global dynamic in terms of R 0 . More specifically, we show that if the basic reproduction number is less than one, then the disease will be extinct, and if the basic reproduction number is larger than one, then the disease will persist. Particularly, our results imply that the nonlocal dispersal of the infected individuals may suppress the spread of the disease even though in a high-risk domain.

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A nonlocal dispersal logistic equation with spatial degeneracy

Cited by 39 publications

References 42 publications

Asymptotic behavior for non-homogeneous nonlocal dispersal equations

Asymptotic behavior for non-homogeneous nonlocal dispersal equations

On eigenvalue problems arising from nonlocal diffusion models

Dynamics of a nonlocal dispersal SIS epidemic model

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