Calculating the Expected Time to Eradicate HIV-1 Using a Markov Chain

Area of Science:

• Mathematical Biology
• Computational Virology
• Epidemiology Modeling

Background:

• Human Immunodeficiency Virus type 1 (HIV-1) infection establishes a persistent reservoir of latently infected cells.
• Complete eradication of HIV-1 requires targeting and eliminating this latent reservoir.
• Accurate estimation of eradication time is crucial for evaluating treatment strategies.

Purpose of the Study:

• To model and calculate the expected time required for complete HIV-1 eradication.
• To investigate the influence of latent cell half-life and initial infected cell count on eradication time.
• To develop a computationally efficient method for solving large-scale Markov chain models.

Main Methods:

• Developed a finite state space continuous-time Markov chain model with two absorbing states: eradication and disaster.
• Calculated expected eradication time by solving systems of linear equations.
• Implemented a novel stop-and-resume technique to manage computational complexity and allow interrupted calculations.

Main Results:

• The expected HIV-1 eradication time is dependent on the half-life of latently infected cells, aligning with previous research.
• With latent cell half-lives ranging from 4.6 to 60 months, predicted eradication times span 4.97 to 31.04 years (SD: 0.64-3.99 years).
• A crucial dependence of eradication time on the initial number of latently infected cells was revealed.

Conclusions:

• The Markov chain model provides a robust framework for estimating HIV-1 eradication timelines.
• Latent cell half-life and initial viral load are critical determinants of the feasibility and duration of eradication.
• The stop-and-resume technique offers a practical solution for computationally intensive modeling in HIV research.