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Khajanchi2017 - Uniform Persistence and Global Stability for a Brain Tumor and Immune System Interaction

ABSTRACT: This paper describes the synergistic interaction between the growth of malignant gliomas and the immune system interactions using a system of coupled ordinary di®erential equations (ODEs). The proposed mathematical model comprises the interaction of glioma cells, macrophages, activated Cytotoxic T-Lymphocytes (CTLs), the immunosuppressive factor TGF- and the immuno-stimulatory factor IFN-. The dynamical behavior of the proposed system both analytically and numerically is investigated from the point of view of stability. By constructing Lyapunov functions, the global behavior of the glioma-free and the interior equilibrium point have been analyzed under some assumptions. Finally, we perform numerical simulations in order to illustrate our analytical ¯ndings by varying the system parameters.

SUBMITTER: Mohammad Umer Sharif Shohan

PROVIDER: BIOMD0000000921 | BioModels | 2024-09-02

REPOSITORIES: BioModels

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	BIOMD0000000921?filename=curation_image.png	Other
	BIOMD0000000921?filename=curation_notes.txt	Txt
	BIOMD0000000921?filename=khajanchi2017-biopax2.owl	Owl
	BIOMD0000000921?filename=khajanchi2017-biopax3.owl	Owl
	BIOMD0000000921?filename=khajanchi2017-matlab.m	Other

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Khajanchi2019 - Stability Analysis of a Mathematical Model forGlioma-Immune Interaction under OptimalTherapy

Project description:Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy Subhas Khajanchi Abstract We investigate a mathematical model using a system of coupled ordinary differential equations, which describes the interplay of malignant glioma cells, macrophages, glioma specific CD8+T cells and the immunotherapeutic drug Adoptive Cellular Immunotherapy (ACI). To better understand under what circumstances the glioma cells can be eliminated, we employ the theory of optimal control. We investigate the dynamics of the system by observing biologically feasible equilibrium points and their stability analysis before administration of the external therapy ACI. We solve an optimal control problem with an objective functional which minimizes the glioma cell burden as well as the side effects of the treatment. We characterize our optimal control in terms of the solutions to the optimality system, in which the state system coupled with the adjoint system. Our model simulation demonstrates that the strength of treatment u1(t) plays an important role to eliminate the glioma cells. Finally, we derive an optimal treatment strategy and then solve it numerically. Keywords: malignant gliomas; stability analysis; optimal control; adoptive cellular immunotherapy

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Gene-expression profiles of PD-L1-affected CD8+ T cells

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