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<p>In order to better understand the mechanisms that control the spread of infectious diseases and thus effectively control the spread of diseases, in the context established by differential inclusion framework, this paper considers a discontinuous incidence function to obtain the periodic solution in a multi-stage disease transmission epidemic system. The positivity and boundedness are proved first. Then, under some assumptions and constraints, we discuss the existence of a periodic solution by using the Kakutani’s theorem of set-valued maps. Furthermore, by using the Lyapunov functional, we investigate the globally exponentially stable (GES) <i>T</i>-periodic solution in finite time. Finally, two examples are discussed to validate the correctness of the theoretical results. The conclusions will help to improve our understanding of the transmission mechanism of infectious diseases, so as to better control and prevent the spread of infectious diseases. The obtained results are new and extend the previous results in the literature.</p>

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Finite Time Attractivity and Exponentially Stable of a Multi-Stage Epidemic System with Discontinuous Incidence

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Wenjie Li,
  • Letian Zhang,
  • Jinde Cao,
  • Fei Xu,
  • Zuowei Cai

摘要

In order to better understand the mechanisms that control the spread of infectious diseases and thus effectively control the spread of diseases, in the context established by differential inclusion framework, this paper considers a discontinuous incidence function to obtain the periodic solution in a multi-stage disease transmission epidemic system. The positivity and boundedness are proved first. Then, under some assumptions and constraints, we discuss the existence of a periodic solution by using the Kakutani’s theorem of set-valued maps. Furthermore, by using the Lyapunov functional, we investigate the globally exponentially stable (GES) T-periodic solution in finite time. Finally, two examples are discussed to validate the correctness of the theoretical results. The conclusions will help to improve our understanding of the transmission mechanism of infectious diseases, so as to better control and prevent the spread of infectious diseases. The obtained results are new and extend the previous results in the literature.