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<p>This paper presents a novel West Nile virus model that has more extensive free boundary conditions and also takes into account the impact of infected mosquitoes on the free boundary, both of which are firsts in West Nile virus modeling. Specifically, the free boundary conditions independent of the dispersal kernel functions in the equations, bring new challenges to the dynamical analysis of spreading-vanishing, especially for the case where the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal R_0\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, which involves new ideas and techniques for dynamics analysis. Moreover, due to the consideration of the impact of infected mosquitoes in the free boundary conditions, new conclusions have been obtained. Numerical schemes have been developed, which not only verify qualitative theoretical results, but also provide novel quantitative insights into the effects of various factors on transmission dynamics. Overall, our results not only differ significantly from the local diffusion version presented in Lin and Zhu (<CitationRef CitationID="CR24">2017</CitationRef>) but also extend all the conclusions from the nonlocal diffusion version in Du and Ni (<CitationRef CitationID="CR16">2020</CitationRef>), with some conclusions obtained under more general conditions.</p>

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A nonlocal West Nile virus model with nonlocal free boundary conditions driven by both mosquitoes and birds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月9日

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  • Xin Long,
  • Yijun Lou,
  • Wenjie Ni,
  • Taishan Yi

摘要

This paper presents a novel West Nile virus model that has more extensive free boundary conditions and also takes into account the impact of infected mosquitoes on the free boundary, both of which are firsts in West Nile virus modeling. Specifically, the free boundary conditions independent of the dispersal kernel functions in the equations, bring new challenges to the dynamical analysis of spreading-vanishing, especially for the case where the basic reproduction number \(\mathcal R_0\le 1\) R 0 ≤ 1 , which involves new ideas and techniques for dynamics analysis. Moreover, due to the consideration of the impact of infected mosquitoes in the free boundary conditions, new conclusions have been obtained. Numerical schemes have been developed, which not only verify qualitative theoretical results, but also provide novel quantitative insights into the effects of various factors on transmission dynamics. Overall, our results not only differ significantly from the local diffusion version presented in Lin and Zhu (2017) but also extend all the conclusions from the nonlocal diffusion version in Du and Ni (2020), with some conclusions obtained under more general conditions.