Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/57756
Title: Rate of accelerated expansion of the epidemic region in a nonlocal epidemic model with free boundaries
Contributor(s): Du, Yihong  (author)orcid ; Ni, Wenjie  (author)orcid ; Wang, Rong (author)
Publication Date: 2023-09-18
DOI: 10.1088/1361-6544/acf63c
Handle Link: https://hdl.handle.net/1959.11/57756
Abstract: 

This paper is concerned with the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the epidemic region is represented by an evolving interval enclosed by the free boundaries in the model. In Wang and Du (2022J. Differ. Eqn. 327 322–81), it was shown that the model is well-posed, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. The spreading speed was investigated in a subsequent work of Wang and Du (2023 Discrete Contin. Dyn. Syst. 43 121–61), where a threshold condition for the diffusion kernels J1 and J2 was obtained, such that the asymptotic spreading speed is finite precisely when this condition is satisfied. In this paper, we examine the case that this threshold condition is not satisfied, which leads to accelerated spreading; for some typical classes of kernel functions, we determine the precise rate of accelerated expansion of the epidemic region by constructing delicate upper and lower solutions.

Publication Type: Journal Article
Grant Details: ARC/DP190103757
Source of Publication: Nonlinearity, v.36, p. 5621-5660
Publisher: Institute of Physics Publishing Ltd
Place of Publication: United Kingdom
ISSN: 1361-6544
0951-7715
Fields of Research (FoR) 2020: 490410 Partial differential equations
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
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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