Wang, Zhiguo; Nie, Hua; Du, Yihong

Author(s)

Wang, Zhiguo

Nie, Hua

Du, Yihong

Publication Date

2024

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.

Citation

European Journal of Applied Mathematics, v.35, p. 462-482

ISSN

1469-4425

0956-7925

Link

https://hdl.handle.net/1959.11/57758

Publisher

Cambridge University Press

Rights

Attribution 4.0 International

Title

Sharp asymptotic profile of the solution to a West Nile virus model with free boundary

Type of document

Journal Article

Entity Type

Publication

Author(s)	Wang, Zhiguo Nie, Hua Du, Yihong
Publication Date	2024
Abstract	<p>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 [<i>g(t), h(t)</i>] in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. <i>J. Math. Biol</i>. 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. <i>J. Math. Biol</i>. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely <i>lim<sub>t→∞</sub> h(t)/t = lim<sub>t→∞</sub> [− g(t)/t] = c<sub>ν</sub></i> , with c<sub>ν</sub></i> 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. <i>J. Math. Biol</i>. 79, 433–466, 2019): we show that <i>h(t) − c<sub>ν</sub>t</i> and <i>g(t) + c<sub>ν</sub>t</i> converge to some constants as <i>t → ∞</i>, 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. </p>
Citation	European Journal of Applied Mathematics, v.35, p. 462-482
ISSN	1469-4425 0956-7925
Link	https://hdl.handle.net/1959.11/57758
Publisher	Cambridge University Press
Rights	Attribution 4.0 International
Title	Sharp asymptotic profile of the solution to a West Nile virus model with free boundary
Type of document	Journal Article
Entity Type	Publication

Sharp asymptotic profile of the solution to a West Nile virus model with free boundary

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