Global Stability Analysis of a Mathematical Model for the "Shock-and-Kill" Strategy in HIV-1/SIV Brain Infection

Area of Science:

• Mathematical Biology
• Virology
• Neuroscience
• Control Theory

Background:

• Human Immunodeficiency Virus (HIV) and Simian Immunodeficiency Virus (SIV) establish persistent infections in central nervous system (CNS) reservoirs.
• The "shock-and-kill" strategy aims to eliminate these reservoirs by reactivating latent viruses and enhancing immune clearance.
• Mathematical models are crucial for understanding the dynamics of HIV/SIV infection and evaluating therapeutic strategies.

Purpose of the Study:

• To provide a rigorous mathematical resolution of the global stability problem for a "shock-and-kill" model of HIV/SIV infection in brain reservoirs.
• To derive an explicit formula for the basic reproduction number ($R_0$) that governs viral eradication or persistence.
• To establish mathematically precise conditions for the efficacy of therapeutic interventions targeting CNS reservoirs.

Main Methods:

• Utilized the next-generation matrix approach combined with an extended graph-theoretic Lyapunov method for multigraphs.
• Developed a refined composite Lyapunov framework to address sign-indefinite quadratic perturbations from parallel transmission arcs.
• Employed systematic asymptotic scaling and multi-parameter tuning to ensure Lyapunov derivative's negative definiteness.

Main Results:

• Derived an explicit formula for the basic reproduction number ($R_0$) as the sole threshold parameter.
• Proved global asymptotic stability of the disease-free equilibrium when $R_0\le 1$.
• Established global asymptotic stability of a unique productive equilibrium when $R_0>1$.

Conclusions:

• The basic reproduction number ($R_0$) definitively determines viral eradication versus persistence in CNS reservoirs.
• The "shock-and-kill" strategy's success is mathematically underpinned, with stability analysis providing a rigorous foundation.
• This work establishes precise mathematical conditions crucial for designing safe and effective interventions against HIV/SIV brain reservoir infections.