This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion-a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infected to a previously chosen level.

Yanni Xiao

Xiaxia Xu

Sanyi Tang

Bulletin of Mathematical Biology

BULLETIN OF MATHEMATICAL BIOLOGY 是数学生物学学会的官方期刊，传播原始研究成果和其他与生物学和数学科学接口相关的信息。贡献应该与这两个领域相关。为了适应广泛的新发展，该期刊接受各种投稿，包括：原创研究文章侧重于借助数学科学工具或新的数学工具和方法获得的新生物学见解，这些工具和方法已证明适用于生物学调查研究数学生物学教育评论评论观点，以及讨论对专业重要的问题的贡献所有贡献都经过同行评审。

The Bulletin of Mathematical Biology is the official journal of the Society for Mathematical Biology, dedicated to disseminating original research findings and information related to the interface between biology and mathematical sciences. Contributions should be relevant to both fields. The journal welcomes a variety of submissions, including original research articles that focus on new biological insights gained through mathematical tools or novel mathematical methods that have proven applicable to biological investigations; reviews on mathematical biology education; and discussions and viewpoints on issues of professional significance. All contributions undergo peer review.

《Bulletin of Mathematical Biology》是数学生物学学会的官方期刊，旨在传播原始研究成果及与生物学和数学科学交叉领域相关的信息。我们欢迎与这两个领域相关的各种投稿，包括：利用数学科学工具或新方法获得的新生物学见解的原创研究文章，这些工具和方法已被证明适用于生物学研究；数学生物学教育的评论；以及对专业重要问题的讨论和观点。所有投稿均经过同行评审。

Sliding Mode Control of Outbreaks of Emerging Infectious Diseases

It is suggested that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infecteds to a previously chosen level.

Category	Quartile
数学	4
数学, 生物学	4
数学, 数学与计算生物学	4

Sliding Mode Control of Outbreaks of Emerging Infectious Diseases

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