A singularly perturbed HIV model with treatment and antigenic variation

Area of Science:

• Mathematical Biology
• Virology
• Dynamical Systems Theory

Background:

• Human Immunodeficiency Virus (HIV) dynamics involve complex interactions between viral load and host cells.
• Existing models often simplify the multiscale nature of HIV progression.
• Therapeutic interventions, such as enzyme inhibitors, introduce further complexity.

Purpose of the Study:

• To develop and analyze a multiscale mathematical model for within-host HIV dynamics.
• To incorporate viral mutation and enzyme inhibitor treatment into the model.
• To simplify the complex system into a lower-dimensional, stable model.

Main Methods:

• Utilized Tikhonov's theorem for singular perturbation analysis.
• Applied Lyapunov's stability theory to prove global asymptotic stability.
• Developed a reduced nonlinear model from a two-time-scale system.

Main Results:

• Demonstrated that the HIV model can be accurately approximated by a lower-dimensional system.
• Proved the global asymptotic stability of the reduced model.
• The simplified model effectively captures long-term HIV dynamics under mutation and treatment.

Conclusions:

• The reduced model provides a computationally tractable yet accurate representation of HIV dynamics.
• This work offers a theoretical foundation for understanding HIV progression and treatment efficacy.
• The stability analysis suggests predictable long-term outcomes for simplified HIV models.