Scholarlink

<p>This paper investigates a cross-diffusion epidemic system in a bounded domain with no-flux boundary conditions. The local and global stability of the positive equilibrium is analyzed for this system without cross-diffusion. Sufficient conditions for the existence and nonexistence of non-constant positive steady states are derived for the cross-diffusion epidemic system, indicating whether pattern formation can occur. The results show that when the self-pressure is strong and the tendency to avoid infection is weak, non-constant positive steady states do not exist. These cases are critical in determining disease persistence. However, non-constant positive steady states arise extensively when the cross-diffusion coefficient for the removed individuals is sufficiently large and the self-diffusion coefficients <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3306_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo stretchy="false">(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$d_{i}(i=1,2)$</EquationSource> </InlineEquation> are relatively small under certain other conditions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The positive steady states of cross-diffusion SIR epidemic system

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月16日

查看全文
  • Chenglin Li,
  • Ming Li,
  • Yunmei Zhao

摘要

This paper investigates a cross-diffusion epidemic system in a bounded domain with no-flux boundary conditions. The local and global stability of the positive equilibrium is analyzed for this system without cross-diffusion. Sufficient conditions for the existence and nonexistence of non-constant positive steady states are derived for the cross-diffusion epidemic system, indicating whether pattern formation can occur. The results show that when the self-pressure is strong and the tendency to avoid infection is weak, non-constant positive steady states do not exist. These cases are critical in determining disease persistence. However, non-constant positive steady states arise extensively when the cross-diffusion coefficient for the removed individuals is sufficiently large and the self-diffusion coefficients d i ( i = 1 , 2 ) $d_{i}(i=1,2)$ are relatively small under certain other conditions.