Canadian Open Mathematical Modeling and Applied Computing Journal
Vol. 1, No. 1, August 2014, pp. 1- 19
Available online at http://crpub.com/Journals.php
Open access
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Research article
Mathematical modeling and analysis of solid cancer
growth with angiogenesis
1
SP. Ganesan,
2
V. Ananthaswamy
*
,
2
L. Rajendran
1
Department of Mathematics, Syed Ammal Engineering College, Ramnad, Tamil Nadu, India
2
Department of Mathematics, The Madura College, Madurai, Tamil Nadu, India.
*
Corresponding author e-mail: ananthu9777@rediffmail.com
Abstract
A mathematical model of solid cancer growth with angiogenesis in the absence of cancer controlling
mechanism has been discussed. The intial conditions supplied to the dynamical system consists of a perturbation in
the form of pulse. The aim of this method is to derive the approximated analytical solution of non-linear differential
equations in the dynamics of cancer growth using the Homotopy perturbation method. Our analytical results are
compared with the numerical simulation and a satisfactory agreement is observed. This method can be easily
extended to solve the strongly nonlinear initial and boundary value problems arising in all applied sciences and
technology problems.
Keywords: Mathematical modeling; Cancer growth; System of nonlinear differential equation; Homotopy
perturbation method; Numerical simulation.
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1. Introduction
Mathematical models of cancer growth have been the subject of research activity for many years. Cancer
arises when within a single cell multiple malfunctions of control systems occur, which are broad, the system that
promote cell growth and the system that protect against erratic growth [1]. In Gompertzian model [2-3], logistic and
power function have been extensively used to describe tumor growth dynamics [4-5]. These simple formalisms have
been also used to investigate different therapeutic strategies such as antiangiogenic or radiation treatments [6].