PDE Models of Virus Replication Coupling 2D Manifold and 3D Volume Effects Evaluated at Realistic Reconstructed Cell Geometries

Markus M. Knodel*, Arne Nägel, Eva Herrmann, Gabriel Wittum

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Virus pandemics and endemics cause enormous pain and costs. Major processes of the intracellular Hepatitis C virus (HCV) viral RNA (vRNA) replication cycle are restricted to the 2D Endoplasmatic Reticulum (ER) manifold, while others take place in the 3D cytosol volume. Modeling the interplay of the major components of the vRNA replication cycle with partial differential equations (PDEs), we establish a system of surface PDEs (sufPDEs) for effects restricted to manifolds coupled to PDEs describing volume effects. Using the diffusion coefficient of viral proteins which we estimated based on experimental data, we discretize the population-dynamics inspired nonlinear diffusion-reaction equation PDE/sufPDE system with the aid of a vertex-centered Finite Volume scheme and evaluate it at unstructured grids representing data based realistic reconstructed cell geometries. We describe the numerical techniques applied and demonstrate the numerical robustness of our simulations. Our framework might contribute to efficient development of antiviral drugs and potent vaccines.

Original languageEnglish (US)
Title of host publicationFinite Volumes for Complex Applications 10—Volume 1, Elliptic and Parabolic Problems - FVCA10, 2023, Invited Contributions
EditorsEmmanuel Franck, Victor Michel-Dansac, Laurent Navoret, Jürgen Fuhrmann
PublisherSpringer
Pages315-323
Number of pages9
ISBN (Print)9783031408632
DOIs
StatePublished - 2023
Event10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023 - Strasbourg, France
Duration: Oct 30 2023Nov 3 2023

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume432
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference10th International Symposium on Finite Volumes for Complex Applications, FVCA10 2023
Country/TerritoryFrance
CityStrasbourg
Period10/30/2311/3/23

Keywords

  • PDEs
  • Vertex centered finite volumes
  • Virus replication

ASJC Scopus subject areas

  • General Mathematics

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