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<p>Age structure is one of the key characteristics of modeling population dynamics and infectious diseases. In this paper, we consider the existence of traveling wave solutions for a physiological age-structured SIR epidemic model with diffusion. Due to the consideration of physiological age of an individual, the wave profile equation of the age-structured model is a nonmonotone parabolic system. To overcome this difficulty, we first study the existence of solutions for our problem in a bounded interval. This proof is mainly based on the comparison principle which allows us to construct suitable sub and super-solutions, and the Schauder’s fixed point theorem. Then, by letting the length of the bounded interval tend to infinity, we establish the existence of traveling wave solutions if the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2024_1219_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {R}}_0&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and the wave speed is greater than the minimal wave speed <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2024_1219_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(c^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>c</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>.</p>

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Propagation Dynamic for a Physiological Age-Structured SIR Epidemic Model with Diffusion

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Xiaoxia Li,
  • Yang Wang,
  • Juping Zhang,
  • Zhen Jin

摘要

Age structure is one of the key characteristics of modeling population dynamics and infectious diseases. In this paper, we consider the existence of traveling wave solutions for a physiological age-structured SIR epidemic model with diffusion. Due to the consideration of physiological age of an individual, the wave profile equation of the age-structured model is a nonmonotone parabolic system. To overcome this difficulty, we first study the existence of solutions for our problem in a bounded interval. This proof is mainly based on the comparison principle which allows us to construct suitable sub and super-solutions, and the Schauder’s fixed point theorem. Then, by letting the length of the bounded interval tend to infinity, we establish the existence of traveling wave solutions if the basic reproduction number \({\mathcal {R}}_0>1\) R 0 > 1 and the wave speed is greater than the minimal wave speed \(c^*\) c ∗ .