Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/63250
Title: Long-time Dynamics Of An Epidemic Model With Nonlocal Diffusion And Free Boundaries: Spreading Speed
Contributor(s): Wang, Rong  (author); Du, Yihong  (author)orcid 
Publication Date: 2023
Early Online Version: 2023
DOI: 10.3934/dcds.2022143
Handle Link: https://hdl.handle.net/1959.11/63250
Abstract: This paper is a sequel to Wang and Du [15], on the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the spreading front is represented by the free boundaries in the model. In [15], it was shown that the model is well-posed, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy; however, the spreading speed was not determined. In this paper, we completely determine the spreading speed of the model when spreading happens. We find a threshold condition for the diffusion kernels J1 and J2 such that the asymptotic spreading speed is finite precisely when this condition is satisfied. Moreover, this speed is determined by a unique semi-wave solution which exists exactly when this threshold condition holds. When this condition is not satisfied, and spreading is successful, we prove that the asymptotic spreading speed is infinite, namely accelerated spreading happens.
Publication Type: Journal Article
Source of Publication: Discrete and Continuous Dynamical Systems, 43(1), p. 121-161
Publisher: Amer Inst Mathematical Sciences-Aims
Place of Publication: United States of America
ISSN: 1553-5231
1078-0947
Fields of Research (FoR) 2020: 4904 Pure mathematics
Socio-Economic Objective (SEO) 2020: tbd
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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