具有饱和发生率的两毒株时滞HIV感染模型的阈值动力学

陈伟; 张龙

doi:10.13568/j.cnki.651094.651316.2021.09.28.0005

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具有饱和发生率的两毒株时滞HIV感染模型的阈值动力学

更新时间：2026-01-21

- 具有饱和发生率的两毒株时滞HIV感染模型的阈值动力学
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 39, Issue 4, Pages: 401-411(2022)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2021.09.28.0005
  CLC： R181;O175
- Published：2022
- 稿件说明：
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[1]陈伟,张龙.具有饱和发生率的两毒株时滞HIV感染模型的阈值动力学[J].新疆大学学报(自然科学版)(中英文),2022,39(04):401-411+420.
[1]陈伟,张龙.具有饱和发生率的两毒株时滞HIV感染模型的阈值动力学[J].新疆大学学报(自然科学版)(中英文),2022,39(04):401-411+420. DOI： 10.13568/j.cnki.651094.651316.2021.09.28.0005.

DOI：10.13568/j.cnki.651094.651316.2021.09.28.0005.

摘要

建立了一类包含药物敏感型和耐药型毒株的HIV感染模型，并且研究了具有饱和发生率和分布潜伏时滞感染模型的动力学行为．得到了模型解的非负性和有界性，以及平衡点的存在性．通过使用线性化方法，构造Lyapunov函数和运用动力系统持续性理论，建立平衡点的局部和全局稳定性，以及模型一致持续性的阈值准则.进一步，数值模拟表明正平衡点全局渐近稳定．

Abstract

This paper establishes an HIV infection model

which includes wild-type and drug-resistant strains

and the dynamic behavior of infection model with saturated incidence and distributed delays is investigated. The nonnegativity and boundedness of solutions

and the existence of equilibria are obtained. The threshold criteria for the local and global asymptotic stability of equilibria and the uniform persistence of the model are established by using the linearization method

constructing Lyapunov functions and applying the theory of persistence in dynamical systems. Moreover

the numerical examples illustrate that the positive equilibrium may be globally asymptotically stable.

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references

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