Numerical schemes for solving and optimizing multiscale models with age of hepatitis C virus dynamics

Area of Science:

• Mathematical biology
• Computational epidemiology
• Virology

Background:

• Age-structured partial differential equation (PDE) models are crucial for understanding viral infections like hepatitis C virus (HCV).
• Solving these complex models numerically presents significant challenges.

Purpose of the Study:

• To investigate and compare numerical solutions of an age-based multiscale HCV model with its long-term analytical approximation during antiviral therapy.
• To assess the suitability of different numerical schemes and optimization techniques for parameter estimation.

Main Methods:

• Development of a flexible numerical solution incorporating integrals from previous iterations.
• Analysis of the stiffness of governing differential equations and numerical scheme stability.
• Comparison of adaptive versus fixed stepsize methods for efficiency.
• Application of numerical optimization for parameter estimation.

Main Results:

• The long-term approximation underestimates the PDE model solution, indicating ignored infection events.
• Stiff differential equations necessitate careful consideration of numerical scheme stability.
• Adaptive stepsize methods offer significant efficiency gains over fixed stepsize methods.
• Numerical optimization effectively estimates parameters directly from the model equations.

Conclusions:

• Advanced numerical solutions that account for previous iterations are essential, challenging the use of standard solvers.
• Efficient and stable numerical methods, such as adaptive stepsize approaches, are critical for simulating complex viral dynamics.
• Numerical optimization provides a viable method for parameter estimation in these models.