Critical-point analysis for three-variable cancer angiogenesis models

DOI10.3934/mbe.2005.2.511zbMath1099.34047OpenAlexW2327766964WikidataQ84007930 ScholiaQ84007930MaRDI QIDQ814663

Yuri Kogan, Yuri Kheifetz, Urszula Fory's

Publication date: 7 February 2006

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mbe.2005.2.511

zbMATH Keywords

stabilitytime delayasymptotic behavior

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Cell biology (92C37) Qualitative investigation and simulation of ordinary differential equation models (34C60) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Asymptotic properties of solutions to ordinary differential equations (34D05)

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Optimal Control of Cancer Treatments: Mathematical Models for the Tumor Microenvironment ⋮ A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy ⋮ The nature of Hopf bifurcation for the Gompertz model with delays ⋮ Analysis of the Hopf bifurcation for the family of angiogenesis models. II: The case of two nonzero unequal delays ⋮ On an extension of a mathematical model for tumor anti-angiogenesis ⋮ What mathematical models can or cannot do in glioma description and understanding ⋮ Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular ``pruning ⋮ Analysis of a delay differential equations modelling tumor growth with angiogenesis ⋮ Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis ⋮ Dynamics and control of a mathematical model for metronomic chemotherapy ⋮ On optimal delivery of combination therapy for tumors

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