Lyapunov functionals for a general time-delayed virus dynamic model with different CTL responses.

Area of Science:

• Mathematical Biology
• Virology
• Immunology

Background:

• Time-delayed virus dynamics models are crucial for understanding infection.
• Nonlinear cytotoxic T lymphocyte (CTL) responses and immune impairment complicate model analysis.
• Previous models often made simplifying assumptions about incidence functions.

Purpose of the Study:

• To propose a novel time-delayed virus dynamics model incorporating general monotonic incidence and distinct nonlinear CTL responses.
• To rigorously analyze the global stability of all equilibria in the presence of immune impairment.
• To address limitations in existing models regarding incidence function derivatives.

Main Methods:

• Development of a time-delayed virus dynamics model with general monotonic incidence.
• Construction of Lyapunov functionals and application of detailed analysis techniques.
• Global asymptotic stability (GAS) analysis for various equilibria.

Main Results:

• Established conditions for the global asymptotic stability of the infection-free equilibrium (E0) when the basic reproduction number (R0) is less than or equal to 1.
• Determined conditions for the global asymptotic stability of the immunity-inactivated infection equilibrium (E1).
• Proved the global asymptotic stability of the immunity-activated infection equilibrium (E+) when it exists.

Conclusions:

• The model provides a more comprehensive framework for studying virus dynamics with complex immune responses.
• The findings offer improved or extended results compared to existing literature.
• The mathematical analysis confirms the stability of different infection states under specific conditions.