Dataset Information

DePillis2005 - A validated mathematical model of cell-mediated immune response to tumor growth

ABSTRACT: This model describes interactions between a tumour and the immune system, with specific emphasis on the role of natural killer and CD8-positive T cells in tumor surveillance. The model features descriptions of tumor-immune cell interactions using ODEs, which allow the prediction of tumor growth, response, and interaction rates.

SUBMITTER: Johannes Meyer

PROVIDER: MODEL1907260001 | BioModels | 2020-11-24

REPOSITORIES: BioModels

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Publications

A validated mathematical model of cell-mediated immune response to tumor growth.

de Pillis Lisette G LG Radunskaya Ami E AE Wiseman Charles L CL

Cancer research 20050901 17

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions desc ...[more]

PMID: 16140967

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Project description:This ordinary differential equation model simulating the interactions between tumor and immune cells is detailed in the publication: Ahmed M. Makhlouf, Lamiaa El-Shennawy, Hesham A. Elkaranshawy, "Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions", Comput Math Methods Med. 2020 Feb 19;2020:7187602. doi: 10.1155/2020/7187602 Comment: This no treatment model is described by equations 1-7 of the publication manuscript. 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.

Dataset Information

DePillis2005 - A validated mathematical model of cell-mediated immune response to tumor growth

Publications

A validated mathematical model of cell-mediated immune response to tumor growth.

Similar Datasets

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