Dynamic analysis of a Filippov blood glucose insulin model

Qiongru Wu; Ling Yu; Xuezhi Li; Wei Li; Qiongru Wu; Ling Yu; Xuezhi Li; Wei Li

doi:10.3934/math.2024895

AIMS Mathematics

2024, Volume 9, Issue 7: 18356-18373. doi: 10.3934/math.2024895

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Research article

Dynamic analysis of a Filippov blood glucose insulin model

1.
School of Mathematics and Statistics, Xinyang College, Xinyang, 464000, Henan, China
2.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, Henan, China
3.
College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, China

Received: 03 February 2024 Revised: 29 April 2024 Accepted: 24 May 2024 Published: 31 May 2024
MSC : 34C60, 92C50, 92D25

This paper proposed a Filippov blood glucose insulin model with threshold control strategy and studied its dynamic properties. Using Filippov's convex method, we proved the global stability of its two subsystems, the existence and conditions of the sliding region of the system were also given, and different types of equilibrium states of the system were also addressed. The existence and stability of pseudo equilibrium points were thoroughly discussed. Through numerical simulations, we have demonstrated that it is possible to effectively control blood sugar concentrations to achieve more cost-effective treatment levels by selecting an appropriate threshold range for insulin injection.
- diabetes,
- pulse system,
- threshold,
- Filippov model
Citation: Qiongru Wu, Ling Yu, Xuezhi Li, Wei Li. Dynamic analysis of a Filippov blood glucose insulin model[J]. AIMS Mathematics, 2024, 9(7): 18356-18373. doi: 10.3934/math.2024895

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Abstract

This paper proposed a Filippov blood glucose insulin model with threshold control strategy and studied its dynamic properties. Using Filippov's convex method, we proved the global stability of its two subsystems, the existence and conditions of the sliding region of the system were also given, and different types of equilibrium states of the system were also addressed. The existence and stability of pseudo equilibrium points were thoroughly discussed. Through numerical simulations, we have demonstrated that it is possible to effectively control blood sugar concentrations to achieve more cost-effective treatment levels by selecting an appropriate threshold range for insulin injection.

References

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