Global stability of age-of-infection multiscale HCV model with therapy

Xiaowen Xiong; Yanqiu Li; Bingliang Li; Xiaowen Xiong; Yanqiu Li; Bingliang Li

doi:10.3934/mbe.2021110

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2182-2205. doi: 10.3934/mbe.2021110

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Research article Special Issues

Global stability of age-of-infection multiscale HCV model with therapy

School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China

Received: 22 November 2020 Accepted: 08 February 2021 Published: 04 March 2021

In order to treat the diseases caused by hepatitis C virus (HCV) more efficiently, the concentration of HCV in blood, cells, tissues and the body has attracted widespread attention from related scholars. This paper studies a dynamic dependent HCV model (more specifically, including age structure and treatment methods model) that concludes states of infection-free and infected equilibrium. Through eigenvalue analysis and Volterra integral formula, it proves that $ E_0 $ is globally asymptotically stable when $ \mathcal{R} < 1 $. After explaining the existence, uniqueness and positive properties of the solution of the system, we have proved the global asymptotic stability of $ E^* $ when $ \mathcal{R} > 1 $ by constructing a suitable Lyapunov function. Through the above proofs, it can be concluded that effective treatment measures can significantly reduce the number of HCVs, so many related researchers are aware of the importance of highly efficient nursing methods and are committed to applying relevant methods to practice.
- multiscale HCV model,
- infection age,
- therapy,
- Lyapunov functional,
- global stability
Citation: Xiaowen Xiong, Yanqiu Li, Bingliang Li. Global stability of age-of-infection multiscale HCV model with therapy[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2182-2205. doi: 10.3934/mbe.2021110

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Abstract

In order to treat the diseases caused by hepatitis C virus (HCV) more efficiently, the concentration of HCV in blood, cells, tissues and the body has attracted widespread attention from related scholars. This paper studies a dynamic dependent HCV model (more specifically, including age structure and treatment methods model) that concludes states of infection-free and infected equilibrium. Through eigenvalue analysis and Volterra integral formula, it proves that $ E_0 $ is globally asymptotically stable when $ \mathcal{R} < 1 $. After explaining the existence, uniqueness and positive properties of the solution of the system, we have proved the global asymptotic stability of $ E^* $ when $ \mathcal{R} > 1 $ by constructing a suitable Lyapunov function. Through the above proofs, it can be concluded that effective treatment measures can significantly reduce the number of HCVs, so many related researchers are aware of the importance of highly efficient nursing methods and are committed to applying relevant methods to practice.

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