| 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
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| ISSN |
1469-4425
0956-7925
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| Link | |
| Language |
en
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| 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
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| Entity Type |
Publication
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| Name | Size | format | Description | Link |
|---|---|---|---|---|
| openpublished/SharpDu2024JournalArticle.pdf | 293.836 KB | application/pdf | Published version | View document |