Persistence and periodicity of survival red blood cells model with time-varying delays and impulses

Tengda Wei; Xiang Xie; Xiaodi Li; Tengda Wei; Xiang Xie; Xiaodi Li

doi:10.3934/mmc.2021002

Mathematical Modelling and Control

2021, Volume 1, Issue 1: 12-25. doi: 10.3934/mmc.2021002

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Research article

Persistence and periodicity of survival red blood cells model with time-varying delays and impulses

1.
School of Mathematical Sciences, Shandong Normal University, Ji'nan, 250014, China
2.
Center for Control and Engineering Computation, Shandong Normal University, Ji'nan 250014, China

Received: 20 February 2021 Accepted: 09 March 2021 Published: 15 March 2021

In this paper, a class of survival red blood cells model with time-varying delays and impulsive effects is considered. First, some sufficient conditions for the persistence are derived by use of the theory on impulsive differential equations. The persistence describes the persistent survival of the mature red blood cells in the mammal under delay and impulsive perturbations. Then assuming that the coefficients in the model are $ \omega $-periodic, some criteria ensuring the existence-uniqueness and global attractivity of positive $ \omega $-periodic solution of the addressed model are obtained, which are suitable for survival red blood cells model with any $ \omega\in \mathbb{R}_+ $. These global attractivity criteria describe the nonexistence of any dynamic diseases in the mammal. Moreover, our proposed results in this paper extend and improve some recent works in the literature. Finally, two examples and their computer simulations are given to show the effectiveness and advantages of the results.
- survival red blood cells model,
- persistence,
- positive stationary oscillation,
- impulsive effects,
- time-varying
Citation: Tengda Wei, Xiang Xie, Xiaodi Li. Persistence and periodicity of survival red blood cells model with time-varying delays and impulses[J]. Mathematical Modelling and Control, 2021, 1(1): 12-25. doi: 10.3934/mmc.2021002

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Abstract

In this paper, a class of survival red blood cells model with time-varying delays and impulsive effects is considered. First, some sufficient conditions for the persistence are derived by use of the theory on impulsive differential equations. The persistence describes the persistent survival of the mature red blood cells in the mammal under delay and impulsive perturbations. Then assuming that the coefficients in the model are $ \omega $-periodic, some criteria ensuring the existence-uniqueness and global attractivity of positive $ \omega $-periodic solution of the addressed model are obtained, which are suitable for survival red blood cells model with any $ \omega\in \mathbb{R}_+ $. These global attractivity criteria describe the nonexistence of any dynamic diseases in the mammal. Moreover, our proposed results in this paper extend and improve some recent works in the literature. Finally, two examples and their computer simulations are given to show the effectiveness and advantages of the results.

References

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