Approximate Analytical Solution of a Cancer Immunotherapy Model by the Application of Differential Transform and Adomian Decomposition Methods

TL;DR

This paper develops approximate analytical solutions for the Kirschner-Panetta cancer immunotherapy model using differential transform and Adomian decomposition methods, providing insights into immune-tumour dynamics.

Contribution

It introduces the application of differential transform and Adomian decomposition methods to solve the nonlinear KP model analytically, which is novel in this context.

Findings

Approximate solutions closely match numerical results.

Methods effectively handle the model's nonlinearity.

Analytical solutions offer deeper understanding of immune-tumour interactions.

Abstract

Immunotherapy plays a major role in tumour treatment, in comparison with other methods of dealing with cancer. The Kirschner-Panetta (KP) model of cancer immunotherapy describes the interaction between tumour cells, effector cells and interleukin-2 which are clinically utilized as medical treatment. The model selects a rich concept of immune-tumour dynamics. In this paper, approximate analytical solutions to KP model are represented by using the differential transform and Adomian decomposition. The complicated nonlinearity of the KP system causes the application of these two methods to require more involved calculations. The approximate analytical solutions to the model are compared with the results obtained by numerical fourth order Runge-Kutta method.