Deformations of acid-mediated invasive tumors in a model with Allee effect
We consider a Gatenby-Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.
Authors
- Arjen Doelman (ORCID: https://orcid.org/0000-0003-4369-4172)
- Peter van Heijster (ORCID: https://orcid.org/0000-0001-6072-3102)
- Philip K. Maini (ORCID: https://orcid.org/0000-0002-0146-9164)
- Paul Carter (ORCID: https://orcid.org/0000-0003-1884-9988)
- Erin Okey
- Paige Yeung
- David Lévy (ORCID: https://orcid.org/0000-0003-0603-0297)
Institutions
- Leiden University (NL)
- Princeton University (US)
- University of California, Irvine (US)
- Brown University (US)
- University of Oxford (GB)
- Irvine University (US)
- Massachusetts Institute of Technology (US)
- Wageningen University & Research (NL)
Publication Details
- Journal
- Journal of Mathematical Biology
- Published
- 2025-05-05
- DOI
- https://doi.org/10.1007/s00285-025-02209-w
- Citations
- 1
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 1.37
Funders
- National Science Foundation
- Universiteit Leiden
- Directorate for Mathematical and Physical Sciences
- University of California, Irvine
- Australian Research Council