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Related Experiment Video

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A Rat Model of EcoHIV Brain Infection

A Rat Model of EcoHIV Brain Infection

Published on: January 21, 2021

Oscillatory viral dynamics in a delayed HIV pathogenesis model.

Yan Wang¹, Yicang Zhou, Jianhong Wu

¹Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, PR China.

Mathematical Biosciences

|March 31, 2009

Summary

This study models HIV infection dynamics with antiretroviral therapy. Time delays in HIV replication can cause oscillations, leading to sustained viral presence even with treatment.

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Chronic, Acute, and Reactivated HIV Infection in Humanized Immunodeficient Mouse Models

Chronic, Acute, and Reactivated HIV Infection in Humanized Immunodeficient Mouse Models

Published on: December 3, 2019

Area of Science:

Mathematical modeling
Virology
Epidemiology

Background:

Antiretroviral therapy (ART) is crucial for managing HIV infection.
HIV replication dynamics and their interaction with treatment are complex.
Understanding disease progression and treatment efficacy requires robust mathematical models.

Purpose of the Study:

To analyze an HIV pathogenesis model that includes antiretroviral therapy and HIV replication time.
To investigate the stability of disease equilibria and the occurrence of Hopf bifurcations.
To determine the impact of time delays on disease dynamics and treatment outcomes.

Main Methods:

Mathematical analysis of differential equations.
Investigation of equilibrium points and their stability.
Bifurcation analysis to identify transitions to oscillatory behavior.

Main Results:

Sufficient conditions for the global stability of the uninfected steady state were derived.
Time delays do not affect the stability of the uninfected state.
Time delays can destabilize the infected steady state, causing Hopf bifurcations to periodic solutions.

Conclusions:

Time delays in HIV replication play a critical role in disease dynamics.
Hopf bifurcations can lead to sustained oscillations, indicating persistent infection despite ART.
Model findings highlight the importance of considering replication time and delays in HIV treatment strategies.