An HIV stochastic model with cell-to-cell infection, B-cell immune response and distributed delay

Area of Science:

• Mathematical modeling
• Virology
• Immunology

Background:

• Human Immunodeficiency Virus (HIV) infection dynamics are complex, involving viral replication, immune responses, and transmission routes.
• Stochastic models are crucial for understanding the inherent randomness in biological systems, including disease progression.
• Cell-to-cell transmission and B-cell immune responses play significant roles in HIV pathogenesis and control.

Purpose of the Study:

• To propose and analyze a delayed HIV stochastic model incorporating virus-to-cell infection, cell-to-cell transmission, and B-cell immune response.
• To investigate the dynamic behavior and stability of the proposed degenerate stochastic differential equation model.
• To identify key parameters influencing HIV dynamics and explore the impact of noise on viral load and immune cell populations.

Main Methods:

• Transformation of a delayed stochastic differential equation into a high-dimensional degenerate stochastic differential equation.
• Rigorous mathematical analysis to establish the existence and uniqueness of the global solution.
• Formulation of Lyapunov functions to determine the existence of a stationary Markov process.
• Application of the law of large numbers and spectral radius analysis for viral clearance conditions.
• Uncertainty and sensitivity analysis to identify critical model parameters.
• Numerical simulations to examine the effects of noise intensity and cell-to-cell infection.

Main Results:

• The existence of a unique global solution for the degenerate HIV model was proven.
• A stationary Markov process exists when the stochastic B-cell-activated reproduction number exceeds one.
• Viral clearance is predicted when the stochastic B-cell-inactivated reproduction number is less than one.
• Key parameters influencing the stochastic B-cell-activated reproduction number were identified through sensitivity analysis.
• Numerical results indicate that low noise levels maintain virus and B-cell populations, while high noise levels promote viral elimination.

Conclusions:

• The developed delayed HIV stochastic model provides insights into viral dynamics and B-cell immune response.
• Noise intensity significantly impacts viral load and immune cell populations, with higher noise levels potentially aiding HIV eradication.
• Cell-to-cell transmission and identified key parameters are crucial factors in determining the effectiveness of the immune response and overall disease progression.