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• 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]

Abstract: The adaptive immune system of a vertebrate may attack its own body, causing autoimmune diseases. Regulatory T cells suppress the activity of the autoreactive effector T cells, but they also interrupt normal immune reactions against foreign antigens. In this paper, we discuss the optimal number of regulatory T cells that should be produced. We make the assumptions that some self-reactive immature T cells may fail to interact with their target antigens during the limited training period and later become effector T cells causing autoimmunity, and that regulatory T cells exist that recognize self-antigens. When a regulatory T cell is stimulated by its target self-antigen on an antigen-presenting cell (APC), it stays there and suppresses the activation of other naive T cells on the same APC. Analysis of the benefit and the harm of having regulatory T cells suggests that the optimal number of regulatory T cells depends on the number of self-antigens, the severity of the autoimmunity, the abundance of pathogenic foreign antigens, and the spatial distribution of self-antigens in the body. For multiple types of self-antigen, we discuss the optimal number of regulatory T cells when the self-antigens are localized in different parts of the body and when they are co-localized. We also examine the separate regulation of the abundances of regulatory T cells for different self-antigens, comparing it with the situation in which they are constrained to be equal. [Copyright &y& Elsevier]

Abstract: The immune system of vertebrates may attack its own body and cause autoimmunity diseases. To prevent autoimmunity, regulatory T cells suppress the activity of the autoreactive effector T cells, but they also interrupt normal immune reactions against foreign antigens. In this paper, we discuss the advantage of having some regulatory T cells by considering the host''s ability of coping with foreign antigens and the harm of autoimmunity. Assumptions are as follows: the immature T cells reactive to abundant self-antigens are eliminated, those reactive to rare self-antigen will become regulatory T cells, and those that fail to interact with the antigens to which they are reactive will become effector T cells. Some self-reactive immature T cells may fail to interact with their own target antigens during the limited training period, and will later become effector T cells, causing autoimmunity. Analysis suggests that, having some regulatory T cells can never be advantageous to the host, if activated regulatory T cells suppress effector T cells at any location of the body (global suppression). In contrast, producing some regulatory T cells can be beneficial, if the body is composed of many compartments and regulatory T cells suppress the immune reactions only within the same compartment (localized suppression). This requires regulatory T cells to stop circulating once they are activated by their own target self-antigens. [Copyright &y& Elsevier]