Dynamic analysis of a bacterial resistance model with impulsive state feedback control

Xiaoxiao Yan; Zhong Zhao; Yuanxian Hui; Jingen Yang; Xiaoxiao Yan; Zhong Zhao; Yuanxian Hui; Jingen Yang

doi:10.3934/mbe.2023903

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 12: 20422-20436. doi: 10.3934/mbe.2023903

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Research article

Dynamic analysis of a bacterial resistance model with impulsive state feedback control

1.
School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China
2.
School of Mathematics and Statistics, Huanghuai University, Zhumadian, Henan 463000, China

Academic Editor: Yang Kuang

Received: 03 September 2023 Revised: 02 October 2023 Accepted: 19 October 2023 Published: 10 November 2023

Bacterial resistance caused by prolonged administration of the same antibiotics exacerbates the threat of bacterial infection to human health. It is essential to optimize antibiotic treatment measures. In this paper, we formulate a simplified model of conversion between sensitive and resistant bacteria. Subsequently, impulsive state feedback control is introduced to reduce bacterial resistance to a low level. The global asymptotic stability of the positive equilibrium and the orbital stability of the order-1 periodic solution are proved by the Poincaré-Bendixson Theorem and the theory of the semi-continuous dynamical system, respectively. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.
- bacterial resistance,
- impulsive state feedback control,
- global asymptotic stability,
- order-1 periodic solution
Citation: Xiaoxiao Yan, Zhong Zhao, Yuanxian Hui, Jingen Yang. Dynamic analysis of a bacterial resistance model with impulsive state feedback control[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20422-20436. doi: 10.3934/mbe.2023903

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Abstract

Bacterial resistance caused by prolonged administration of the same antibiotics exacerbates the threat of bacterial infection to human health. It is essential to optimize antibiotic treatment measures. In this paper, we formulate a simplified model of conversion between sensitive and resistant bacteria. Subsequently, impulsive state feedback control is introduced to reduce bacterial resistance to a low level. The global asymptotic stability of the positive equilibrium and the orbital stability of the order-1 periodic solution are proved by the Poincaré-Bendixson Theorem and the theory of the semi-continuous dynamical system, respectively. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.

References

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