Scholarlink

<p>This study investigates the impact of individual movement and saturated treatment on the spatio-temporal dynamics of an infectious disease through an SIR reaction-diffusion model with self-diffusion under zero-flux boundary conditions. The well-posedness of the proposed model, including the existence, positivity, and boundedness of solutions, is established using partial differential equation techniques. The corresponding ODE system is analyzed for local stability, Hopf bifurcation, and Bautin bifurcation via normal form theory and Lyapunov coefficients. In addition, the spatial model is examined for diffusion-driven instabilities, including Hopf, Turing, and Turing-Hopf bifurcations. Numerical simulations performed using a finite difference scheme reveal the emergence of diverse spatial patterns such as holes, stripes, and mixed structures, which validate the theoretical findings. The results demonstrate how diffusion and saturated treatment influence disease persistence, oscillatory behavior, and spatial pattern formation in epidemic dynamics.</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

Exploring the Impact of Saturated Treatment on Spatial Patterns via a Reduced SIR Model Analysis

  • 期刊论文

  • 发表日期：

    2026年7月24日

查看全文
  • Arun Kumar,
  • R. P. Gupta

摘要

This study investigates the impact of individual movement and saturated treatment on the spatio-temporal dynamics of an infectious disease through an SIR reaction-diffusion model with self-diffusion under zero-flux boundary conditions. The well-posedness of the proposed model, including the existence, positivity, and boundedness of solutions, is established using partial differential equation techniques. The corresponding ODE system is analyzed for local stability, Hopf bifurcation, and Bautin bifurcation via normal form theory and Lyapunov coefficients. In addition, the spatial model is examined for diffusion-driven instabilities, including Hopf, Turing, and Turing-Hopf bifurcations. Numerical simulations performed using a finite difference scheme reveal the emergence of diverse spatial patterns such as holes, stripes, and mixed structures, which validate the theoretical findings. The results demonstrate how diffusion and saturated treatment influence disease persistence, oscillatory behavior, and spatial pattern formation in epidemic dynamics.