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

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.