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<p>In this paper, we consider a reaction-diffusion SIRS epidemic model with standard incidence in a homogeneous environment. We first investigate the boundedness of the solutions. Then, with this help of Lyapunov functionals, we provide sufficient conditions on the exponential convergence of the disease-free equilibrium and the endemic equilibrium. We also support these theoretical results with numerical simulations.</p>

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Exponential convergence of a diffusive SIRS epidemic model with standard incidence

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Wenjie Li,
  • Ying Zhang,
  • Qian Ding,
  • Jianshe Yu

摘要

In this paper, we consider a reaction-diffusion SIRS epidemic model with standard incidence in a homogeneous environment. We first investigate the boundedness of the solutions. Then, with this help of Lyapunov functionals, we provide sufficient conditions on the exponential convergence of the disease-free equilibrium and the endemic equilibrium. We also support these theoretical results with numerical simulations.