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<p>This paper concerns a nonlocal diffusive SIR epidemic model with nonlocal infectious and double free boundaries, which can be used to describe the spreading of infectious diseases. This model is a strongly coupled nonlocal diffusion system in some sense. We mainly study criteria for spreading and vanishing, and the long time behaviors. In addition to the usual <i>Basic Reproduction Number</i> <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1234_Article_IEq1.gif" Format="GIF" Height="28" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {R}_0=\frac{k(a-\beta )}{b(a+\gamma )}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mi>k</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>-</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>b</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </math></EquationSource> </InlineEquation>, we also discover another number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1234_Article_IEq2.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="166" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathscr {R}}_0\left( k\frac{a-\beta }{b}, \cdot , (-h_0,h_0)\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mfenced close=")" open="("> <mi>k</mi> <mfrac> <mrow> <mi>a</mi> <mo>-</mo> <mi>β</mi> </mrow> <mi>b</mi> </mfrac> <mo>,</mo> <mo>·</mo> <mo>,</mo> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <msub> <mi>h</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>h</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, and find that these two numbers play a crucial role in determining both spreading and vanishing.</p>

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Dynamics of a Nonlocal Diffusive and Infectious SIR Epidemic Model with Double Free Boundaries

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Hanxiang Bao,
  • Mingxin Wang

摘要

This paper concerns a nonlocal diffusive SIR epidemic model with nonlocal infectious and double free boundaries, which can be used to describe the spreading of infectious diseases. This model is a strongly coupled nonlocal diffusion system in some sense. We mainly study criteria for spreading and vanishing, and the long time behaviors. In addition to the usual Basic Reproduction Number \(\mathcal {R}_0=\frac{k(a-\beta )}{b(a+\gamma )}\) R 0 = k ( a - β ) b ( a + γ ) , we also discover another number \({\mathscr {R}}_0\left( k\frac{a-\beta }{b}, \cdot , (-h_0,h_0)\right) \) R 0 k a - β b , · , ( - h 0 , h 0 ) , and find that these two numbers play a crucial role in determining both spreading and vanishing.