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In this article we analytically solve the
Itik-Banks tumor growth model by means of a recent technique for strongly
nonlinear problems - the step homotopy analysis method (SHAM). This
analytical algorithm, based on a modification of the standard homotopy
analysis method (HAM) initially proposed by Liao, allows us to obtain a
one-parameter family of explicit series solutions for the studied cancer
model. These solutions describe the temporal dynamics of tumor cells
interacting with healthy host cells and effector immune cells. The
artificial parameter involved in the analytical method is particularly
important, providing us with an elegant way to ensure convergent series
solutions. Our analytical results are found to be in excellent agreement
with the numerical simulations. We use the obtained analytical solutions to
investigate the role of immune system activation due to antigen recognition.
We found that an increase in the stimulation of immune cells by tumor cells
makes the system to enter into chaotic dynamics. Our results are discussed
in the context of tumor cells dynamics and persistence, as well as in the
possible therapeutic consequences of the identified dynamics. |
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