Stochastic models for virus and immune system dynamics.

Area of Science:

• Mathematical Biology
• Virology
• Immunology

Background:

• Deterministic models of viral infections, like Human Immunodeficiency Virus-1 (HIV-1), often predict persistent infection.
• These models typically consider populations of uninfected cells, infected cells, and virus particles.
• Incorporating immune response factors and stochasticity is crucial for a more realistic understanding of early infection dynamics.

Purpose of the Study:

• To develop novel stochastic models for viral infection and immune response dynamics in early infection stages.
• To investigate the probability of viral extinction using continuous-time Markov chain (CTMC) models.
• To compare insights from stochastic models with traditional deterministic approaches.

Main Methods:

• Derived stochastic differential equations (SDEs) and CTMC models from deterministic ordinary differential equation frameworks.
• Incorporated variability in cellular processes, infection, immune activation, and viral reproduction (budding vs. bursting).
• Calculated the basic reproduction number (R0) for deterministic models and performed numerical simulations for stochastic models using HIV-1 parameters.

Main Results:

• Deterministic models predict persistent infection when R0 > 1.
• Stochastic models demonstrate a non-zero probability of viral extinction, even when R0 > 1.
• The probability of successful viral invasion is contingent upon initial viral dose, immune system activation status, and viral release strategy (bursting or budding).

Conclusions:

• Stochastic models offer distinct insights into early viral dynamics compared to deterministic models.
• Viral extinction is a possible outcome, challenging predictions of inevitable persistence.
• Early-stage infection outcomes are sensitive to initial conditions and biological mechanisms like viral release strategies.