Chemotaxis-driven stationary and oscillatory patterns in a diffusive HIV-1 model with CTL immune response and general...

Area of Science:

• Mathematical Biology
• Virology
• Immunology

Background:

• Investigating the Human Immunodeficiency Virus type 1 (HIV-1) model dynamics is crucial for understanding disease progression.
• The role of cytotoxic T lymphocyte (CTL) immune response and chemotaxis in HIV-1 spread requires detailed mathematical analysis.

Purpose of the Study:

• To analyze a reaction-diffusion-chemotaxis HIV-1 model incorporating CTL immune response and general sensitivity.
• To establish global classical solvability and boundedness for the model in arbitrary dimensions.
• To investigate the conditions under which chemotaxis induces spatiotemporal patterns, affecting steady states.

Main Methods:

• Global existence and boundedness analysis for the reaction-diffusion-chemotaxis model.
• Analysis of spatiotemporal dynamics of three steady states: infection-free (S0), CTL-inactivated (S1), and CTL-activated (S*).
• Investigation of the impact of chemotactic sensitivity on pattern formation, including Turing and oscillatory patterns.

Main Results:

• Global classical solvability and L∞-boundedness are proven for the HIV-1 model in bounded domains.
• The stability of steady states (S0, S1, S*) is determined by the basic reproduction number (R0).
• Chemotaxis can destabilize the CTL-activated steady state (S*), leading to stationary Turing patterns or irregular oscillatory patterns.

Conclusions:

• The study provides a rigorous mathematical framework for understanding HIV-1 dynamics with immune response and chemotaxis.
• Chemotaxis plays a significant role in generating complex spatiotemporal patterns, influencing disease dynamics.
• Different chemotactic response functions can alter the system's overall dynamics, highlighting the importance of detailed modeling.