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Modeling a Tumor Growth with Piecewise Constant Arguments
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-14
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This study is based on an early brain tumor growth that is modeled as a hybrid system such as (A): dx(t)/dt=x(t){r(1-αx(t)-β0x(⟦t⟧)-β1x(⟦t-1⟧))+γ1x(⟦t⟧)+γ2x(⟦t-1⟧)}, where the parameters α, β0, β1, and r denote positive numbers, γ1 and γ2 are negative numbers and ⟦t⟧ is the integer part of t∈[0,∞).
Equation (A) explains a brain tumor growth, where γ1 is embedded to show the drug effect on the tumor and γ2 is a rate that causes a negative effect by the immune system on the tumor population.
Using (A), we have constructed two models of a tumor growth: one is (A) and the other one is a population model at low density by incorporating an Allee function to (A) at time t.
To consider the global behavior of (A), we investigate the discrete solutions of (A).
Examination of the characterization of the stability shows that increase of the population growth rate decreases the local stability of the positive equilibrium point of (A).
The simulations give a detailed description of the behavior of solutions of (A) with and without Allee effect.
American Psychological Association (APA)
Bozkurt, F.. 2013. Modeling a Tumor Growth with Piecewise Constant Arguments. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-502531
Modern Language Association (MLA)
Bozkurt, F.. Modeling a Tumor Growth with Piecewise Constant Arguments. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-502531
American Medical Association (AMA)
Bozkurt, F.. Modeling a Tumor Growth with Piecewise Constant Arguments. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-502531
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-502531