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<p>This paper studies the threshold dynamics and optimal control problem of a stochastic SIR epidemic model considering disease prevention awareness. The obtained results have a positive effect on the effective prevention and control of infectious diseases. Specifically, the existence and uniqueness of the global positive solution of the model are established first. Then, the sufficient conditions for disease extinction and persistence are deeply investigated. Under the condition of disease persistence, the ergodicity of the model solution is further examined. Finally, based on the actual needs of infectious disease prevention and control, an optimal control problem is proposed, and the explicit form of the optimal control strategy is derived by applying the Pontryagin maximum principle. All theoretical results are verified through numerical simulations.</p>

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Long-term behaviors and optimal control of a novel stochastic epidemic model

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Jing Ji,
  • Min Zhou,
  • Huili Xiang

摘要

This paper studies the threshold dynamics and optimal control problem of a stochastic SIR epidemic model considering disease prevention awareness. The obtained results have a positive effect on the effective prevention and control of infectious diseases. Specifically, the existence and uniqueness of the global positive solution of the model are established first. Then, the sufficient conditions for disease extinction and persistence are deeply investigated. Under the condition of disease persistence, the ergodicity of the model solution is further examined. Finally, based on the actual needs of infectious disease prevention and control, an optimal control problem is proposed, and the explicit form of the optimal control strategy is derived by applying the Pontryagin maximum principle. All theoretical results are verified through numerical simulations.