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      Mathematical Modelling for the Role of CD4 +T Cells in Tumor-Immune Interactions

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          Abstract

          Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8 +T cells, but they neglected the role of CD4 +T cells. Other models were constructed to study the role of CD4 +T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4 +T cells, CD8 +T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge–Kutta method failed to solve it. Consequently, the “Adams predictor-corrector” method is used. The results reveal that the patient's immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4 +T cells can be an alternative to both CD8 +T cell therapy and cytokines in some cases. Moreover, CD4 +T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4 +T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8 +T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients' treatment intervention strategies.

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          Most cited references 54

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          Role of bone marrow-derived cells in presenting MHC class I-restricted tumor antigens.

          Many tumors express tumor-specific antigens capable of being presented to CD8+ T cells by major histocompatibility complex (MHC) class I molecules. Antigen presentation models predict that the tumor cell itself should present these antigens to T cells. However, when conditions for the priming of tumor-specific responses were examined in mice, no detectable presentation of MHC class I-restricted tumor antigens by the tumor itself was found. Rather, tumor antigens were exclusively presented by host bone marrow-derived cells. Thus, MHC class I-restricted antigens are efficiently transferred in vivo to bone marrow-derived antigen-presenting cells, which suggests that human leukocyte antigen matching may be less critical in the application of tumor vaccines than previously thought.
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            The mathematics of cancer: integrating quantitative models.

            Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
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              Cytokines in clinical cancer immunotherapy

              Cytokines are soluble proteins that mediate cell-to-cell communication. Based on the discovery of the potent anti-tumour activities of several pro-inflammatory cytokines in animal models, clinical research led to the approval of recombinant interferon-alpha and interleukin-2 for the treatment of several malignancies, even if efficacy was only modest. These early milestones in immunotherapy have been followed by the recent addition to clinical practice of antibodies that inhibit immune checkpoints, as well as chimeric antigen receptor T cells. A renewed interest in the anti-tumour properties of cytokines has led to an exponential increase in the number of clinical trials that explore the safety and efficacy of cytokine-based drugs, not only as single agents, but also in combination with other immunomodulatory drugs. These second-generation drugs under clinical development include known molecules with novel mechanisms of action, new targets, and fusion proteins that increase half-life and target cytokine activity to the tumour microenvironment or to the desired effector immune cells. In addition, the detrimental activity of immunosuppressive cytokines can be blocked by antagonistic antibodies, small molecules, cytokine traps or siRNAs. In this review, we provide an overview of the novel trends in the cytokine immunotherapy field that are yielding therapeutic agents for clinical trials.
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                Author and article information

                Contributors
                Journal
                Comput Math Methods Med
                Comput Math Methods Med
                CMMM
                Computational and Mathematical Methods in Medicine
                Hindawi
                1748-670X
                1748-6718
                2020
                19 February 2020
                : 2020
                Affiliations
                1Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt
                2Institute of Graduate Studies and Research, Alexandria University, Alexandria, Egypt
                Author notes

                Academic Editor: David Diller

                Article
                10.1155/2020/7187602
                7049850
                5c00b1cc-dcc4-4dfa-9a5c-308dd31d7708
                Copyright © 2020 Ahmed M. Makhlouf et al.

                This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                Categories
                Research Article

                Applied mathematics

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