Dynamics of a within-host drug resistance model with impulsive state feedback control

Jing Jia; Yanfeng Zhao; Zhong Zhao; Bing Liu; Xinyu Song; Yuanxian Hui; Jing Jia; Yanfeng Zhao; Zhong Zhao; Bing Liu; Xinyu Song; Yuanxian Hui

doi:10.3934/mbe.2023103

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 2219-2231. doi: 10.3934/mbe.2023103

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Research article

Dynamics of a within-host drug resistance model with impulsive state feedback control

1.
School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China
2.
School of Information Science and Technology, Northwest University, Xi'an, Shaanxi 710127, China
3.
School of Mathematics and Statistics, Huanghuai University, Zhumadian, Henan 463000, China
4.
School of Mathematics and Information Science, Anshan Normal University, Anshan, Liaoning 114007, China

Academic Editor: Yang Kuang

Received: 22 July 2022 Revised: 06 November 2022 Accepted: 21 October 2022 Published: 17 November 2022

Bacterial resistance poses a major hazard to human health, and is caused by the misuse and overuse of antibiotics. Thus, it is imperative to investigate the optimal dosing strategy to improve the treatment effect. In this study, a mathematical model of antibiotic-induced resistance is presented to improve the antibiotic effectiveness. First, conditions for the global asymptotical stability of the equilibrium without pulsed effect are given according to the Poincaré-Bendixson Theorem. Second, a mathematical model of the dosing strategy with impulsive state feedback control is also formulated to reduce drug resistance to an acceptable level. The existence and stability of the order-1 periodic solution of the system are discussed to obtain the optimal control of antibiotics. Finally, our conclusions are confirmed by means of numerical simulations.
- Poincaré-Bendixson theorem,
- optimal dosing strategy,
- order-1 periodic solution,
- semi-continuous dynamical system
Citation: Jing Jia, Yanfeng Zhao, Zhong Zhao, Bing Liu, Xinyu Song, Yuanxian Hui. Dynamics of a within-host drug resistance model with impulsive state feedback control[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 2219-2231. doi: 10.3934/mbe.2023103

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Abstract

Bacterial resistance poses a major hazard to human health, and is caused by the misuse and overuse of antibiotics. Thus, it is imperative to investigate the optimal dosing strategy to improve the treatment effect. In this study, a mathematical model of antibiotic-induced resistance is presented to improve the antibiotic effectiveness. First, conditions for the global asymptotical stability of the equilibrium without pulsed effect are given according to the Poincaré-Bendixson Theorem. Second, a mathematical model of the dosing strategy with impulsive state feedback control is also formulated to reduce drug resistance to an acceptable level. The existence and stability of the order-1 periodic solution of the system are discussed to obtain the optimal control of antibiotics. Finally, our conclusions are confirmed by means of numerical simulations.

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