Mathematical analysis of a tumour-immune interaction model : a moving boundary problem
| dc.contributor.author | Malinzi, Joseph | |
| dc.contributor.author | Amima, Innocenter | |
| dc.date.accessioned | 2019-08-13T08:23:32Z | |
| dc.date.issued | 2019-02 | |
| dc.description.abstract | A spatio-temporal mathematical model, in the form of a moving boundary problem, to explain cancer dormancy is developed. Analysis of the model is carried out for both temporal and spatio-temporal cases. Stability analysis and numerical simulations of the temporal model replicate experimental observations of immune-induced tumour dormancy. Travelling wave solutions of the spatio-temporal model are determined using the hyperbolic tangent method and minimum wave speeds of invasion are calculated. Travelling wave analysis depicts that cell invasion dynamics are mainly driven by their motion and growth rates. A stability analysis of the spatio-temporal model shows a possibility of dynamical stabilization of the tumour-free steady state. Simulation results reveal that the tumour swells to a dormant level. | en_ZA |
| dc.description.department | Mathematics and Applied Mathematics | en_ZA |
| dc.description.embargo | 2020-02-01 | |
| dc.description.librarian | hj2019 | en_ZA |
| dc.description.uri | https://www.elsevier.com/locate/mbs | en_ZA |
| dc.identifier.citation | Malinzi, J. & Amima, I. 2019, 'Mathematical analysis of a tumour-immune interaction model : a moving boundary problem', Mathematical Biosciences, vol. 308, pp. 8-19. | en_ZA |
| dc.identifier.issn | 0025-5564 (print) | |
| dc.identifier.issn | 1879-3134 (online) | |
| dc.identifier.other | 10.1016/j.mbs.2018.12.009 | |
| dc.identifier.uri | http://hdl.handle.net/2263/71089 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | Elsevier | en_ZA |
| dc.rights | © 2018 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Mathematical Biosciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Mathematical Biosciences, vol. 308, pp. 8-19, 2019. doi : 10.1016/j.mbs.2018.12.009. | en_ZA |
| dc.subject | Moving boundary problem | en_ZA |
| dc.subject | Cancer dormancy | en_ZA |
| dc.subject | Tumour-immune interactions | en_ZA |
| dc.subject | Travelling wave solutions | en_ZA |
| dc.subject | Hyperbolic tangent method | en_ZA |
| dc.subject | Tumour radius | en_ZA |
| dc.title | Mathematical analysis of a tumour-immune interaction model : a moving boundary problem | en_ZA |
| dc.type | Postprint Article | en_ZA |