Bio-algorithms for the modeling and simulation of cancer cells and the immune response

Abstract There have been significant developments in clinical, experimental, and theoretical approaches to understand the biomechanics of tumor cells and immune cells. Cytotoxic T lymphocytes (CTLs) are regarded as a major antitumor mechanism of immune cells. Mathematical modeling of tumor growth is an important and useful tool to observe and understand clinical phenomena analytically. This work develops a novel two-variable mathematical model to describe the interaction of tumor cells and CTLs. The designed model is providing an integrated framework to investigate the complexity of tumor progression and answer clinical questions that cannot always be reached with experimental tools. The parameters of the model are estimated from experimental study and stability analysis of the model is performed through nullclines. A global sensitivity analysis is also performed to check the uncertainty of the parameters. The results of numerical simulations of the model support the importance of the CTLs and demonstrate that CTLs can eliminate small tumors. The proposed model provides efficacious information to study and demonstrate the complex dynamics of breast cancer.