Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/57758
Title: Sharp asymptotic profile of the solution to a West Nile virus model with free boundary
Contributor(s): Wang, Zhiguo (author); Nie, Hua (author); Du, Yihong  (author)orcid 
Publication Date: 2024
Early Online Version: 2023
Open Access: Yes
DOI: 10.1017/S0956792523000281
Handle Link: https://hdl.handle.net/1959.11/57758
Abstract: 

We consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval [g(t), h(t)] in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J. Math. Biol. 75, 1381–1409, 2017). The asymptotic spreading speed of the front has been determined in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely limt→∞ h(t)/t = limt→∞ [− g(t)/t] = cν , with cν the speed of the semi-wave solution. In this paper, by employing new techniques, we significantly improve the estimate in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019): we show that h(t) − cνt and g(t) + cνt converge to some constants as t → ∞, and the solution of the model converges to the semi-wave solution. The results also apply to a wide class of analogous Ross–MacDonold epidemic models.

Publication Type: Journal Article
Grant Details: ARC/DP190103757
Source of Publication: European Journal of Applied Mathematics, v.35, p. 462-482
Publisher: Cambridge University Press
Place of Publication: United Kingdom
ISSN: 1469-4425
0956-7925
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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