### Abstract

This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection-free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle's invariance principle shows that if the model's basic reproductive number R<inf>0</inf> < 1, the infection-free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R<inf>0</inf> = 1. The basic reproductive number R<inf>0</inf> of the modified model is independent of plasma total CD4<sup>+</sup> T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas-De-León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients' anti-HIV infection treatments. The simulation results have shown that the first 4 weeks' treatments made the two group patients' R'<inf>0</inf> < 1, respectively. After the period, drug resistance made the two group patients' R'<inf>0</inf> > 1. The results explain why the two group patients' mean CD4<sup>+</sup> T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.

Original language | English (US) |
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Pages (from-to) | 95-103 |

Number of pages | 9 |

Journal | IET Systems Biology |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2015 |

### ASJC Scopus subject areas

- Biotechnology
- Cell Biology
- Genetics
- Molecular Biology
- Modeling and Simulation