Two-stage model of carcinogenic mutations with the influence of delays

Urszula Foryś; Beata Zduniak

doi:10.3934/dcdsb.2014.19.2501

Article Contents

2014, Volume 19, Issue 8: 2501-2519. Doi: 10.3934/dcdsb.2014.19.2501

This issue Previous Article Existence of weak solutions for non-local fractional problems via Morse theory Next Article Parameter estimation of systems with delays via structural sensitivity analysis

Two-stage model of carcinogenic mutations with the influence of delays

Urszula Foryś^1, and
Beata Zduniak^2,

1.
University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 Warsaw
2.
Warsaw University of Life Science, Faculty of Applied Informatics and Mathematics, Nowoursynowska 159, 02-776 Warsaw

Received: October 31, 2013

Revised: March 31, 2014

Published: September 2014

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Abstract

In the paper we make an attempt to study the influence of time delays combined with diffusion on the dynamics of two-stage carcinogenic mutations model. Included delays represent time needed for transformation from one type of cells to the other one. In the presented analysis we focus on possible stability switches due to increasing delays and diffusion driven instability. It occurs that diffusion has no significant impact on asymptotic behaviour of the model solutions, while one of the present delays has destabilising effect in most of cases we study. Analytical results are illustrated by numerical examples of the model dynamics.

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Mathematics Subject Classification: Primary: 34K20, 34K28, 37G35, 37N25; Secondary: 92B05, 92B25, 92C50.

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