Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay.

Area of Science:

• Mathematical Biology
• Epidemiology
• Virology

Background:

• Understanding within-host COVID-19 dynamics is crucial for developing effective treatments.
• Previous models often simplify the complex interplay of virus, host cells, and immune responses.
• Stochastic factors and time delays significantly influence disease progression.

Purpose of the Study:

• To formulate a novel mathematical model for within-host COVID-19 dynamics.
• To analyze the impact of discrete delays and noise on disease progression.
• To investigate conditions for disease extinction versus persistence within the human body.

Main Methods:

• Development of a stochastic mathematical model incorporating Target, Latent, Infected, and Virus-free states.
• Establishment of positivity and uniqueness of model solutions.
• Stability analysis of disease-free and endemic equilibria to determine disease outcomes.

Main Results:

• The model demonstrates conditions for both the extinction and persistence of COVID-19 within a host.
• Analysis reveals the significant impact of delay tactics and stochastic noise on disease extinction.
• Crucially, stochasticity enables disease extinction even in scenarios where deterministic models predict an inevitable pandemic.

Conclusions:

• Stochastic modeling provides a more nuanced understanding of within-host COVID-19 dynamics.
• Noise and delays can be critical factors in achieving viral clearance.
• This research offers insights into potential therapeutic strategies that leverage these factors for disease control.