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<p>In this paper, we present a novel stochastic SIVS epidemic model with proportional vaccination. The most prominent innovation of this work lies in the introduction of a non-autonomous infectious disease model with time delay, which is distinct from traditional stochastic infectious disease models. This unique model enables in-depth exploration of the transmission patterns and prevention strategies for seasonal infectious diseases such as influenza, mumps, malaria, and dengue fever. For the proposed stochastic system, we initially prove its well-posedness by rigorously demonstrating the global existence and uniqueness of the positive solution. Subsequently, we derive a series of sufficient conditions for the extinction and persistence of the disease. Moreover, by leveraging Khaminskii’s boundary periodic Markov processes, we establish the existence of a non-trivial positive periodic solution within the system. Finally, comprehensive numerical simulations are carried out to systematically analyze the effects of perturbations on the epidemic model. These findings not only enrich the theoretical framework of epidemic modeling but also provide valuable insights for practical disease prevention and control.</p>

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Analysis of a Stochastic Delayed SIVS Epidemic Model with Seasonal Variation

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Xiang-yun Shi,
  • Xue-yong Zhou,
  • Yi-meng Cao

摘要

In this paper, we present a novel stochastic SIVS epidemic model with proportional vaccination. The most prominent innovation of this work lies in the introduction of a non-autonomous infectious disease model with time delay, which is distinct from traditional stochastic infectious disease models. This unique model enables in-depth exploration of the transmission patterns and prevention strategies for seasonal infectious diseases such as influenza, mumps, malaria, and dengue fever. For the proposed stochastic system, we initially prove its well-posedness by rigorously demonstrating the global existence and uniqueness of the positive solution. Subsequently, we derive a series of sufficient conditions for the extinction and persistence of the disease. Moreover, by leveraging Khaminskii’s boundary periodic Markov processes, we establish the existence of a non-trivial positive periodic solution within the system. Finally, comprehensive numerical simulations are carried out to systematically analyze the effects of perturbations on the epidemic model. These findings not only enrich the theoretical framework of epidemic modeling but also provide valuable insights for practical disease prevention and control.