Enhancing viral dynamics modeling: reliable initial estimation and validity conditions for quasi-steady state...

Area of Science:

• Virology
• Mathematical Biology
• Computational Science

Background:

• Mathematical models are crucial for understanding viral dynamics, with the basic viral model widely used for infection kinetics.
• Quasi-steady-state approximation (QSSA) is often applied to simplify viral models and improve computational efficiency.
• Existing viral QSSA models contain a flaw where they incorrectly assume infected cells and viruses evolve on the same timescale, leading to inaccurate simplifications.

Purpose of the Study:

• To develop a revised QSSA viral model that accurately accounts for timescale separation between infected cells and viruses.
• To address and correct the erroneous loss of infected cell initial values during model reduction in existing QSSA models.
• To establish a validity condition for the accurate application of QSSA in viral dynamics.

Main Methods:

• Developed a revised QSSA viral model incorporating correct timescale separation.
• Introduced a mathematical method for estimating the initial condition of infected cells.
• Defined a validity condition ($C_v=\delta /c$) for QSSA accuracy, requiring $C_v\ll 1$.

Main Results:

• The revised QSSA model prevents the loss of infected cell initial values, maintaining biological fidelity.
• Comparative analysis demonstrated improved predictive accuracy and computational efficiency over existing models.
• Sensitivity analysis confirmed the revised model's robustness and preservation of key dynamic responses.
• Parameter estimation showed more accurate recovery of true parameter values under strong timescale separation.

Conclusions:

• The revised QSSA viral model resolves a critical flaw in existing models, enabling more accurate and consistent viral dynamics modeling.
• Correcting the infected cell loss issue provides a robust framework for virological applications, especially with limited experimental data.
• The findings support the use of the revised QSSA for reliable viral dynamics analysis and prediction.