Journal article
A multiscale theory for network advection-reaction-diffusion
- Abstract:
- Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), e.g. the spread of an infectious agent between different countries, or the transport and replication of toxic proteins across different brain regions in neurodegenerative diseases. In these models, transport is modelled at the macroscale through an operator, the so-called graph Laplacian based on the edge properties and topology, capturing the fluxes between different nodes of the network. However, this phenomenological approach fails to take into account the physical processes taking place at the microscale within the edge. A fundamental problem is then to obtain a transport operator from mechanistic principles based on the underlying transport process. Using advection-reaction-diffusion as a generic mechanism for inter-nodal exchanges, we derive a multiscale network transport model and derive the corresponding linear transport operator at the macroscale from first principles. This effective graph Laplacian is fully determined by the transport mechanisms along the edges at the microscale. We show that this operator correctly captures the transport, and we study its scaling properties with respect to edge length.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, pdf, 653.1KB, Terms of use)
-
- Publisher copy:
- 10.1007/s00285-026-02386-2
Authors
- Publisher:
- Springer Nature
- Journal:
- Journal of Mathematical Biology More from this journal
- Volume:
- 92
- Issue:
- 5
- Article number:
- 65
- Publication date:
- 2026-04-09
- Acceptance date:
- 2026-03-17
- DOI:
- EISSN:
-
1432-1416
- ISSN:
-
0303-6812
- Language:
-
English
- Pubs id:
-
2390480
- Local pid:
-
pubs:2390480
- Deposit date:
-
2026-03-17
- ARK identifier:
Terms of use
- Copyright holder:
- Oliveri et al
- Copyright date:
- 2026
- Rights statement:
- © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
If you are the owner of this record, you can report an update to it here: Report update to this record