Scholarlink

<p>In this work, we construct Lyapunov functionals to analyze the global stability of the equilibria in reaction-diffusion systems arising in biological models. We employ Lyapunov functionals originally constructed for associated ordinary differential equation (ODE) models and extend them to partial differential equation (PDE) systems involving spatial diffusion. We analyze disease-free and endemic equilibrium stability in terms of the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_9761_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathscr {R}}_0\)</EquationSource> </InlineEquation> a threshold parameter. Specifically, we show that when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_9761_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathscr {R}}_0&lt;1\)</EquationSource> </InlineEquation> the disease-free equilibrium is globally asymptotically stable, while for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_9761_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathscr {R}}_0&gt; 1\)</EquationSource> </InlineEquation> the endemic equilibrium is globally stable under certain conditions. To make our methods more feasible, we supply some examples from epidemiology and good health, including spatially structured models with diffusion. Numerical simulations are provided to justify the theoretical results and to show the convergence behavior of the solutions.</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

Mathematical exploration of a diffusive infection’s dynamics and simulation

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月26日

查看全文
  • Rassim Darazirar,
  • Ahmed A. Mohsen,
  • Aziz Khan,
  • Manar A. Alqudah,
  • Thabet Abdeljawad,
  • Rajermani Thinakaran

摘要

In this work, we construct Lyapunov functionals to analyze the global stability of the equilibria in reaction-diffusion systems arising in biological models. We employ Lyapunov functionals originally constructed for associated ordinary differential equation (ODE) models and extend them to partial differential equation (PDE) systems involving spatial diffusion. We analyze disease-free and endemic equilibrium stability in terms of the basic reproduction number \({\mathscr {R}}_0\) a threshold parameter. Specifically, we show that when \({\mathscr {R}}_0<1\) the disease-free equilibrium is globally asymptotically stable, while for \({\mathscr {R}}_0> 1\) the endemic equilibrium is globally stable under certain conditions. To make our methods more feasible, we supply some examples from epidemiology and good health, including spatially structured models with diffusion. Numerical simulations are provided to justify the theoretical results and to show the convergence behavior of the solutions.