Numerical Schemes for Solving and Optimizing Multiscale Models with Age of Hepatitis C Virus Dynamics

Details

• Alternative Title:
  Math Biosci
• Personal Author:
  Reinharz, Vladimir ; Dahari, Harel ; Barash, Danny
• Description:
  Age-structured PDE models have been developed to study viral infection and treatment. However, they are notoriously difficult to solve. Here, we investigate the numerical solutions of an age-based multiscale model of hepatitis C virus (HCV) dynamics during antiviral therapy and compare them with an analytical approximation, namely its long-term approximation. First, starting from a simple yet flexible numerical solution that also considers an integral approximated over previous iterations, we show that the long-term approximation is an underestimate of the PDE model solution as expected since some infection events are being ignored. We then argue for the importance of having a numerical solution that takes into account previous iterations for the associated integral, making problematic the use of canned solvers. Second, we demonstrate that the governing differential equations are stiff and the stability of the numerical scheme should be considered. Third, we show that considerable gain in efficiency can be achieved by using adaptive stepsize methods over fixed stepsize methods for simulating realistic scenarios when solving multiscale models numerically. Finally, we compare between several numerical schemes for the solution of the equations and demonstrate the use of a numerical optimization scheme for the parameter estimation performed directly from the equations.
• Subjects:
  Anti-Retroviral Agents Hepacivirus HIV Infections Humans Models, Biological Time Factors
• Keywords:
  Adaptive Stepsize Integration Age-structured Model Hepatitis C Virus Multiscale Model Numerical Solution Partial Differential Equations
• Source:
  Math Biosci. 300:1-13
• Pubmed ID:
  29550297
• Pubmed Central ID:
  PMC5992100
• Document Type:
  Journal Article
• Funding:
  R01 AI078881/AI/NIAID NIH HHSUnited States/ ; R01 GM121600/GM/NIGMS NIH HHSUnited States/ ; U51 PS004607/PS/NCHHSTP CDC HHSUnited States/
• Volume:
  300
• Collection(s):
  CDC Public Access
• Main Document Checksum:
  urn:sha256:c6e9564e4a0f2317e0f203c884cfa587651ea8dc15ac80b57ea822a7afd4eec6
• Download URL:
  https://stacks.cdc.gov/view/cdc/151798/cdc_151798_DS1.pdf
• File Type:
  [PDF - 744.57 KB ]