Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/31761
Title: The dynamics of a degenerate epidemic model with nonlocal diffusion and free boundaries
Contributor(s): Zhao, Meng (author); Zhang, Yang (author); Li, Wan-Tong (author); Du, Yihong  (author)orcid 
Publication Date: 2020-08-05
Early Online Version: 2020-03-05
DOI: 10.1016/j.jde.2020.02.029
Handle Link: https://hdl.handle.net/1959.11/31761
Abstract: 

We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and infected humans in return contribute to the growth of the agents. The model can be viewed as a nonlocal version of the free boundary model studied by Ahn, Beak and Lin, with its origin tracing back to Capasso et al. We prove that the problem has a unique solution defined for all t > 0, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local diffusion model in. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the model of, where the spreading has finite speed whenever spreading happens.

Publication Type: Journal Article
Grant Details: ARC/DP190103757
Source of Publication: Journal of Differential Equations, 269(4), p. 1-30
Publisher: Academic Press
Place of Publication: United States of America
ISSN: 1090-2732
0022-0396
Fields of Research (FoR) 2020: 490102 Biological mathematics
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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