THREE TYPES OF SIMPLE DDE'S DESCRIBING TUMOR GROWTH

DOI10.1142/S0218339007002313zbMath1151.92015OpenAlexW2141533782WikidataQ112197637 ScholiaQ112197637MaRDI QIDQ3530555

Marek Bodnar, Urszula Fory's

Publication date: 20 October 2008

Published in: Journal of Biological Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218339007002313

zbMATH Keywords

Hopf bifurcationdelay differential equationlogistic modelGompertz modelEhrlich Ascites tumorGreenspan modelvon Foerster equations

Mathematics Subject Classification ID

Medical applications (general) (92C50) Stability theory of functional-differential equations (34K20) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18)

Related Items

On immunotherapies and cancer vaccination protocols: a mathematical modelling approach, The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay, Analysis of the Hopf bifurcation for the family of angiogenesis models. II: The case of two nonzero unequal delays, Stability analysis of the family of tumour angiogenesis models with distributed time delays, About a generalized model of lymphoma, Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular ``pruning, Delay Differential Equations in Bio-Populations, Tractable Model of Malignant Gliomas Immunotherapy with Discrete Time Delays, Logistic Tumor Growth with Delay and Impulsive Treatment, Logistic Equation with Treatment Function and Discrete Delays, Introducing delay dynamics to Bertalanffy's spherical tumour growth model, Stochastic resonance in a tumor-immune system subject to bounded noises and time delay, Optimal control of the dynamics of a tumor growth model with Hollings' type-II functional response, Global stability analysis of some nonlinear delay differential equations in population dynamics, Close encounters of the cell kind: the impact of contact inhibition on tumour growth and cancer models, A Mathematical Model of Gene Therapy for the Treatment of Cancer, Multi-dimensional Lotka-Volterra systems for carcinogenesis mutations

Cites Work

• Optimal scheduling for cell synchronization by cycle-phase-specific blockers
• Delay differential equations: with applications in population dynamics
• Mathematical model of cancer chemotherapy. Periodic schedules of phase- specific cytotoxic-agent administration increasing the selectivity of therapy
• Reduction of cytotoxicity to normal tissues by new regimens of cell-cycle phase-specific drugs
• The effect of time delays on the dynamics of avascular tumor growth
• The nonnegativity of solutions to delay differential equations
• Mathematical biology. Vol. 1: An introduction.
• Global stability for a class of delay differential equations.
• Environmental stochasticity of gompertz model with time delay
• Models for the Growth of a Solid Tumor by Diffusion
• Unnamed Item