Oscillations and bistability in the dynamics of cytotoxic reactions mediated by the response of immune cells to solid tumours

DOI10.1016/j.mcm.2007.02.026zbMath1148.92019OpenAlexW2000766165MaRDI QIDQ955510

I. El Akili, Olivier Lejeune, Mark A. J. Chaplain

Publication date: 20 November 2008

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2007.02.026

zbMATH Keywords

immune responsesolid tumour growthdormancy

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Medical applications (general) (92C50) Cell biology (92C37) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (10)

A direct RBF-PU method for simulating the infiltration of cytotoxic T-lymphocytes into the tumor microenvironment ⋮ Continuation along bifurcation branches for a tumor model with a necrotic core ⋮ Multi-stability and multi-instability phenomena in a mathematical model of tumor-immune-virus interactions ⋮ Interactions between the immune system and cancer: A brief review of non-spatial mathematical models ⋮ Mathematical modeling on helper T cells in a tumor immune system ⋮ Dual role of delay effects in a tumour–immune system ⋮ Nonlinear dynamics in tumor-immune system interaction models with delays ⋮ Mathematical modeling and dynamic analysis of anti-tumor immune response ⋮ Space-velocity thermostatted kinetic theory model of tumor growth ⋮ A NEW MATHEMATICAL MODELING AND SUB-OPTIMAL CHEMOTHERAPY OF CANCER

Cites Work

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• Approximate Michaelis-Menten kinetics displayed in a stochastic model of cell-mediated cytotoxicity
• On the kinectics and optimal specificity of cytotoxic reactions mediated by T-lymphocyte clones
• Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis
• Dynamics of tumor interaction with the host immune system
• The modelling of the immune competition by generalized kinetic (Boltzmann) models: Review and research perspectives
• Modelling and mathematical problems related to tumor evolution and its interaction with the immune system
• Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumor-immune cells competition
• The dynamics of growth-factor-modified immune response to cancer growth: One dimensional models
• STRATEGIES OF APPLIED MATHEMATICS TOWARDS AN IMMUNO-MATHEMATICAL THEORY ON TUMORS AND IMMUNE SYSTEM INTERACTIONS
• Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour
• MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION
• Modelling Macrophage Infiltration into Avascular Tumours
• MATHEMATICAL MODELLING OF MACROPHAGE DYNAMICS IN TUMOURS
• Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy
• Mathematical models of therapeutical actions related to tumour and immune system competition

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