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<p>An impulsive SIR epidemic model characterized by an incidence rate governed by a mean-reverting Ornstein–Uhlenbeck process is investigated in this paper. First, the existence and uniqueness of the global positive solution to the impulsive SIR epidemic model are established by constructing an equivalent system without impulses. Second, a criterion for assessing the extinction of the epidemic is derived by introducing a periodic function. Then, the existence and global attraction of the boundary periodic solution are demonstrated using the comparison theorem, and a sufficient condition for the existence of a positive periodic solution is obtained with the aid of a Lyapunov function. Finally, the theoretical results are validated via a series of numerical simulations.</p>

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Periodic solutions of an impulsive SIR epidemic model incorporating a mean-reverting Ornstein–Uhlenbeck process for the incidence rate

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月10日

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  • Xiaochen Ma,
  • Qi Yao,
  • Daqing Jiang

摘要

An impulsive SIR epidemic model characterized by an incidence rate governed by a mean-reverting Ornstein–Uhlenbeck process is investigated in this paper. First, the existence and uniqueness of the global positive solution to the impulsive SIR epidemic model are established by constructing an equivalent system without impulses. Second, a criterion for assessing the extinction of the epidemic is derived by introducing a periodic function. Then, the existence and global attraction of the boundary periodic solution are demonstrated using the comparison theorem, and a sufficient condition for the existence of a positive periodic solution is obtained with the aid of a Lyapunov function. Finally, the theoretical results are validated via a series of numerical simulations.