Analysis of HIV models with two time delays

Area of Science:

• Mathematical Biology
• Virology
• Immunology

Background:

• Mathematical models are crucial for understanding Human Immunodeficiency Virus (HIV) infection dynamics.
• Time delays in biological processes can significantly alter model predictions.
• Previous models may not fully capture the complex temporal aspects of HIV infection.

Purpose of the Study:

• To investigate the impact of two distinct time delays on HIV infection dynamics using mathematical modeling.
• To analyze the stability of steady states in models incorporating HIV latency and immune responses.
• To evaluate how time delays influence viral replication and immune control in HIV infection.

Main Methods:

• Development and analysis of two mathematical models for HIV infection, each with two time delays.
• Definition of the basic reproductive number to assess disease spread.
• Analysis of local and global stability of model equilibrium points.
• Numerical simulations to explore the influence of time delays on infection dynamics.
• Derivation of stability crossing curves for models with immune response delays.

Main Results:

• In the HIV latency model, time delays were shown to affect the stability of steady states.
• Numerical simulations demonstrated the significant influence of time delays on predicted HIV infection dynamics.
• For the HIV immune response model, stability crossing curves were obtained, revealing complex behavior with two positive delays.
• These curves indicate critical thresholds where model stability changes.

Conclusions:

• Time delays are critical parameters that must be accurately incorporated into mathematical models of HIV infection.
• The timing of events, such as latency establishment and immune response emergence, profoundly affects HIV dynamics.
• Mathematical modeling with careful consideration of time delays provides valuable insights into controlling viral replication and managing HIV infection.