Mathematical analysis of a tumour-immune interaction model : a moving boundary problem
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Date
Authors
Malinzi, Joseph
Amima, Innocenter
Journal Title
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Volume Title
Publisher
Elsevier
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.
Description
Keywords
Moving boundary problem, Cancer dormancy, Tumour-immune interactions, Travelling wave solutions, Hyperbolic tangent method, Tumour radius
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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.