A hepatitis C virus infection model with time-varying drug effectiveness: solution and analysis

Area of Science:

• Virology
• Mathematical Biology
• Pharmacokinetics

Background:

• Antiviral therapy models often assume constant drug effectiveness.
• Realistic models consider time-varying or concentration-dependent drug effectiveness.

Purpose of the Study:

• To mathematically analyze a varying-effectiveness (VE) model for hepatitis C virus (HCV) infection therapy.
• To derive an analytic solution for the VE model and fit it to patient data.

Main Methods:

• Transformed the linear VE model into a Bessel equation.
• Derived an analytic solution using modified Bessel functions.
• Fitted the model solution to clinical data from HCV-infected patients.

Main Results:

• The VE model, though linear, lacks a closed-form solution due to time-varying effectiveness.
• Biologically realistic parameters predict biphasic viral decay, similar to constant-effectiveness (CE) models.
• Developed a method to determine decay phase transition points using maximum curvature.

Conclusions:

• The derived analytic solution for the VE model provides a more realistic representation of antiviral therapy.
• The rate of second-phase decay is linked to infected cell death and maximum therapy effectiveness.
• First-phase decay rates depend on multiple parameters, including the rate of effectiveness increase over time.