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DePillis2008 - Optimal control of mixed immunotherapy and chemotherapy of tumors

ABSTRACT: <notes xmlns="http://www.sbml.org/sbml/level2/version4"> <body xmlns="http://www.w3.org/1999/xhtml"> <pre>Optimal control of mixed immunotherapy and chemotherapy of tumors Lisette Depillis, K. R. Fister , W. Gu, Tiffany Head, Kenny Maples, Todd Neal, Anand Murugan and Kenji Kozai Abstract We investigate a mathematical population model of tumor-immune interactions. Thepopulations involved are tumor cells, specific and non-specific immune cells, and con-centrations of therapeutic treatments. We establish the existence of an optimal con-trol for this model and provide necessary conditions for the optimal control triple forsimultaneous application of chemotherapy, tumor infiltrating lymphocyte (TIL) ther-apy, and interleukin-2 (IL-2) treatment. We discuss numerical results for the combina-tion of the chemo-immunotherapy regimens. We find that the qualitative nature of ourresults indicates that chemotherapy is the dominant intervention with TIL interactingin a complementary fashion with the chemotherapy. However, within the optimal con-trol context, the interleukin-2 treatment does not become activated for the estimatedparameter ranges.

SUBMITTER: Mohammad Umer Sharif Shohan

PROVIDER: BIOMD0000000913 | BioModels | 2024-09-02

REPOSITORIES: BioModels

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			Action	DRS
	BIOMD0000000913?filename=dePillis2008.cps	Other
	BIOMD0000000913?filename=dePillis2008.sedml	Other
	BIOMD0000000913?filename=dePillis2008.xml	Xml

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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.

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DePillis2008 - Optimal control of mixed immunotherapy and chemotherapy of tumors

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