An accurate two-phase approximate solution to an acute viral infection model

Area of Science:

• Virology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Acute viral infections exhibit distinct growth and decay phases, often visualized linearly on a log scale.
• Traditional viral dynamic models are complex and nonlinear, making analytical solutions challenging.
• Approximations are valuable for understanding viral kinetics, especially given the exponential nature of solutions.

Purpose of the Study:

• To derive and validate a two-phase approximate solution for the target cell-limited influenza model.
• To analyze the relationship between model parameters, viral peaks, and decay rates.
• To explore the utility of this approximate model in understanding antiviral treatments and host-virus interactions.

Main Methods:

• Derivation of a two-phase approximate analytical solution for viral dynamics.
• Application of the model to influenza A data from six patients.
• Comparison of model predictions with patient data to assess accuracy and identify deviations.
• Development of an alternate approximation for cases with non-conforming decay phases.

Main Results:

• The derived two-phase model accurately approximates viral growth and decay in most cases.
• Expressions were determined for viral growth rate, peak involvement of parameters, and decay rate.
• One patient's data required an alternate approximation, highlighting potential model limitations or unique viral kinetics.
• The model provides a framework for analyzing parameters influencing viral load.

Conclusions:

• A simplified, two-phase approximate model can effectively describe viral dynamics during acute infections.
• The model facilitates the analysis of key parameters governing viral load, offering insights into infection progression.
• This approach has potential applications in evaluating antiviral therapies and understanding variations in host-pathogen interactions.