Stability analysis and persistence of a phage therapy model

Ei Ei Kyaw; Hongchan Zheng; Jingjing Wang; Htoo Kyaw Hlaing; Ei Ei Kyaw; Hongchan Zheng; Jingjing Wang; Htoo Kyaw Hlaing

doi:10.3934/mbe.2021280

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5552-5572. doi: 10.3934/mbe.2021280

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Research article Special Issues

Stability analysis and persistence of a phage therapy model

School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China

Academic Editor: Zhongwei Shen

Received: 25 April 2021 Accepted: 10 June 2021 Published: 21 June 2021

This study deals with a phage therapy model involving nonlinear interactions of the bacteria–phage–innate immune response. The main aim of this work is to analytically and numerically examine the dynamic behavior of the phage therapy model. First, we investigate the positivity and boundedness of the system. Second, we analyze the existence and local asymptotic stability of different equilibrium solutions. Third, we investigate the global stability for equilibrium without immune system and equilibrium without phages, and coexistence equilibrium by means of the Bendixson–Dulac criterion and the Lyapunov functional method, respectively. Furthermore, we discuss the persistence and nonpersistence of the system under some conditions. Finally, we perform numerical simulations to substantiate the results obtained in this research.
- phage therapy model,
- persistence,
- extinction,
- stability,
- Lyapunov functional
Citation: Ei Ei Kyaw, Hongchan Zheng, Jingjing Wang, Htoo Kyaw Hlaing. Stability analysis and persistence of a phage therapy model[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5552-5572. doi: 10.3934/mbe.2021280

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Abstract

This study deals with a phage therapy model involving nonlinear interactions of the bacteria–phage–innate immune response. The main aim of this work is to analytically and numerically examine the dynamic behavior of the phage therapy model. First, we investigate the positivity and boundedness of the system. Second, we analyze the existence and local asymptotic stability of different equilibrium solutions. Third, we investigate the global stability for equilibrium without immune system and equilibrium without phages, and coexistence equilibrium by means of the Bendixson–Dulac criterion and the Lyapunov functional method, respectively. Furthermore, we discuss the persistence and nonpersistence of the system under some conditions. Finally, we perform numerical simulations to substantiate the results obtained in this research.

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