Jacoby last multiplier and group theoretic approaches to a model describing breast cancer stem cells

Abstract

Despite the complexity of tumour cells population, which is well known as difficult to control. Mathematical modelling has been identified as a powerful tool to understand complex dynamics and integrations of tumour cells population. In this paper, the technique of Jacobi Last Multiplier is employed to build linear Lagrangians of cancer stem cells (CSC) which describe the development dynamic of CSC population in vitro as well as in vivo. Additionally, the use of Noether’s theorem facilitate in achieving conservation laws of the reduced two dimensional nonlinear system. The technique of Lie Symmetry is applied to a model and helps to point out the correlation between parameters. As a result, the system has been linearized and the corresponding analytical as well as numerical solutions were provided.