Virus dynamics model with intracellular delays and immune response

Area of Science:

• Mathematical Biology
• Virology
• Dynamical Systems

Background:

• Human Immunodeficiency Virus type 1 (HIV-1) infection dynamics are complex.
• Previous models by Pawelek et al. studied intracellular and immune response delays.
• Uninfected CD4+ T-cell logistic growth is crucial for viral dynamics.

Purpose of the Study:

• To incorporate logistic growth for uninfected CD4+ T-cells into an existing HIV-1 model.
• To analyze the impact of intracellular and immune response delays on viral persistence and stability.
• To investigate complex dynamics arising from these model modifications.

Main Methods:

• Mathematical modeling of HIV-1 infection.
• Analysis of steady states and global asymptotic stability.
• Investigation of uniform persistence and basic reproduction number (R0).
• Application of Hopf bifurcation theory and normal form analysis for delay-induced oscillations.
• Numerical simulations to explore chaotic dynamics and bifurcation diagrams.

Main Results:

• The infection-free steady state is globally stable if R0 < 1.
• The viral system is uniformly persistent if R0 > 1.
• Delays can destabilize the infected steady state, causing Hopf bifurcations and stable periodic oscillations.
• Numerical simulations reveal chaotic oscillations and complex viral load bifurcation diagrams.

Conclusions:

• The basic reproduction number (R0) critically determines viral clearance or persistence.
• Time delays (intracellular and immune response) can destabilize the infected state, leading to complex dynamics.
• The logistic growth term for CD4+ T-cells, combined with delays, generates rich and potentially chaotic viral load behavior.