Stability analysis for HIV infection delay model with protease inhibitor.

Area of Science:

• Mathematical modeling
• Virology
• Pharmacology

Background:

• Human Immunodeficiency Virus type 1 (HIV-1) infection is a significant global health concern.
• Protease inhibitor (PI) therapy is a cornerstone of antiretroviral treatment for HIV-1.
• Understanding the dynamics of viral load fluctuations, such as viral blips, is crucial for optimizing treatment strategies.

Purpose of the Study:

• To develop and analyze a mathematical model of HIV-1 infection incorporating protease inhibitor therapy and multiple time delays.
• To numerically approximate the frequency of bifurcating periodic solutions and the critical threshold value for treatment efficacy.
• To compare the model's predicted oscillation frequencies with clinically observed viral blips.

Main Methods:

• A mathematical model simulating HIV-1 infection dynamics under protease inhibitor therapy was formulated.
• The model incorporated three distinct time delays representing biological processes.
• Numerical methods were employed to approximate the threshold value and the frequency of periodic solutions.

Main Results:

• The numerical approximation yielded a realistic threshold value for the effectiveness of protease inhibitor therapy.
• The frequency of oscillations predicted by the model aligned with the frequencies of viral blips observed in patients.
• The model demonstrates the potential for complex dynamics, including periodic solutions, in HIV-1 infection under therapy.

Conclusions:

• The developed mathematical model provides a valuable tool for understanding HIV-1 dynamics during protease inhibitor therapy.
• The consistency between model predictions and clinical observations (viral blips) supports the model's validity.
• The findings suggest that incorporating time delays is essential for accurately capturing the oscillatory behavior of viral load in treated HIV-1 patients.