Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. (English) Zbl 1467.35323
In Section 1, the authors provide a short review of existing models with multiple taxis performed by (at least) one species obtained.
In Section 2, the authors consider a new mathematical model for tumor invasion, which includes two mutually exclusive cellular phenotypes (migrating and such that distribute).
The paper proves the global existence of weak solutions of the simplified version of the model and performed numerical simulations for complete tuning for several phenotypes switching and mobility scenarios. (Section 3)
The authors also compared (using modeling) with the model with the corresponding haptotaxis-chemotaxis containing indirect chemorepellant production (Section 4).
In Section 5, the authors discuss the results obtained.
In Section 2, the authors consider a new mathematical model for tumor invasion, which includes two mutually exclusive cellular phenotypes (migrating and such that distribute).
The paper proves the global existence of weak solutions of the simplified version of the model and performed numerical simulations for complete tuning for several phenotypes switching and mobility scenarios. (Section 3)
The authors also compared (using modeling) with the model with the corresponding haptotaxis-chemotaxis containing indirect chemorepellant production (Section 4).
In Section 5, the authors discuss the results obtained.
Reviewer: Yaroslav Baranetskij (Lviv)
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 92C37 | Cell biology |
| 35K55 | Nonlinear parabolic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35D30 | Weak solutions to PDEs |
| 92-08 | Computational methods for problems pertaining to biology |
Keywords:
multiple taxis and review of models; tumor invasion; interspecies repellence; global existence; numerical simulationsSoftware:
MatlabReferences:
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