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Related Experiment Video

Updated: Mar 27, 2026

Humanized NOD/SCID/IL2rγnull (hu-NSG) Mouse Model for HIV Replication and Latency Studies
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A delayed HIV-1 model with virus waning term.

Bing Li1, Yuming Chen, Xuejuan Lu

  • 1Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, 3041#, 2 Yi-Kuang street, Harbin, 150080, China.

Mathematical Biosciences and Engineering : MBE
|January 19, 2016
PubMed
Summary

This study models delayed HIV-1 infection, revealing that ignoring time delays and virus waning underestimates infection risk and alters viral load dynamics. Delays significantly impact disease progression.

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Area of Science:

  • Mathematical Biology
  • Immunology
  • Virology

Background:

  • Human Immunodeficiency Virus type 1 (HIV-1) infection involves complex interactions between the virus and the host's immune system.
  • Understanding the temporal dynamics of viral replication and immune response is crucial for predicting disease progression.

Purpose of the Study:

  • To analyze a mathematical model of HIV-1 infection incorporating CTL immune response and virus waning with discrete time delays.
  • To investigate the impact of these delays on the stability and persistence of HIV-1 infection.

Main Methods:

  • Development and analysis of a delayed differential equation model for HIV-1 infection.
  • Calculation of the basic reproduction number (R0) to determine infection thresholds.
  • Analysis of steady states, uniform persistence, and Hopf bifurcation.

Main Results:

  • The infection-free steady state is stable if R0 < 1, leading to viral clearance.
  • If R0 > 1, the system exhibits uniform persistence, maintaining a constant viral load.
  • Hopf bifurcation indicates complex dynamics, and delays significantly influence infection risk and viral load.

Conclusions:

  • Time delays in viral production and immune response critically affect HIV-1 infection dynamics.
  • Virus waning and delays must be considered to accurately assess infection risk and predict viral load.
  • The model highlights the importance of temporal factors in understanding HIV-1 pathogenesis.