Studying the importance of regulatory T cells in chemoimmunotherapy mathematical modeling and proposing new approaches for developing a mathematical dynamic of cancer.

• A model is proposed based on the key role of Regulatory T cells in chemoimmunotherapy. • The model's fixed points are obtained and the bifurcation diagrams are discussed. • New features of personalizing a cancer mathematical model are presented. • Considering Regulatory T cells leads to identifying critical patient conditions more precisely. Studying the mathematical dynamics of cancer has gained the attention of bioengineers in the past three decades. Different kinds of modelling considering various aspects of treatment have been proposed. In this paper, the key role of Regulatory T cells is discussed and a model in ordinary differential equation (ODE) form is proposed by adding this state to the system dynamics considering chemoimmunotherapy treatment. Regulatory T cells are considered as one of the main tumor cells' tactics to deceive the body's immune system. The improved model is verified mathematically and biologically and fits all criteria in both fields. The results show that entering Regulatory T cells state on cancer mathematical modelling for simulating body cells for chemoimmunotherapy provides a way to identify critical cases more carefully, which a simplified model is unable to accomplish. This point emphasizes the fact that this state must be present in cancer modelling to anticipate immune response more accurately. The advanced system fixed points are obtained by the Newton method and bifurcation diagrams are derived and discussed. New features and remarks are proposed during the journey of developing more accurate models that have the best fit with laboratory data. The sensitivity chart of the model is illustrated and novel aspects of discussions are made with the aim of personalizing a model for a patient and identifying critical conditions based on the chart before any treatment begins. This point enables physicians to determine whether critical conditions have occurred for a patient in a specific treatment or not. [ABSTRACT FROM AUTHOR]