Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999)

From MaRDI portal
Publication:1886332

DOI10.1016/j.mbs.2004.06.003zbMath1050.92039OpenAlexW4382645197WikidataQ44050049 ScholiaQ44050049MaRDI QIDQ1886332

Alberto d'Onofrio, Alberto Gandolfi

Publication date: 18 November 2004

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

Full work available at URL: https://doi.org/10.1016/j.mbs.2004.06.003



Related Items

Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy, Evaluating the efficacies of maximum tolerated dose and metronomic chemotherapies: a mathematical approach, Understanding the antiangiogenic effect of metronomic chemotherapy through a simple mathematical model, Some applications of periodic orbits for competitive systems, Mathematical model of cancer growth controled by metronomic chemotherapies, Dynamic aspects of tumour–immune system interaction under a periodic immunotherapy, Modeling tumor growth inhibition and toxicity outcome after administration of anticancer agents in xenograft mice: a dynamic energy budget (DEB) approach, An optimal control approach for the treatment of solid tumors with angiogenesis inhibitors, Bifurcation of Nontrivial Periodic Solutions for a Food Chain Beddington–DeAngelis Interference Model with Impulsive Effect, The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation, Angiogenesis model with Erlang distributed delays, Local controllability and optimal control for a model of combined anticancer therapy with control delays, Optimal Control of Cancer Treatments: Mathematical Models for the Tumor Microenvironment, A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy, The Structure of Optimal Protocols for a Mathematical Model of Chemotherapy with Antiangiogenic Effects, Stability and controllability issues in mathematical modeling of the intensive treatment of leukemia, Optimization of combined leukemia therapy by finite-dimensional optimal control modeling, Traveling waves and free boundaries arising in tumor angiogenesis, The nature of Hopf bifurcation for the Gompertz model with delays, Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments, Modeling of tumor growth incorporating the effects of necrosis and the effect of Bevacizumab, Analysis of the Hopf bifurcation for the family of angiogenesis models. II: The case of two nonzero unequal delays, Combination of antiangiogenic treatment with chemotherapy as a multi‐input optimal control problem, Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function, Stability analysis of the family of tumour angiogenesis models with distributed time delays, On an extension of a mathematical model for tumor anti-angiogenesis, Tumour growth control: analysis of alternative approaches, A dynamic programming approach for approximate optimal control for cancer therapy, What mathematical models can or cannot do in glioma description and understanding, Closed-loop control of tumor growth by means of anti-angiogenic administration, Theoretical investigation of the efficacy of antiangiogenic drugs combined to chemotherapy in xenografted mice, Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular ``pruning, Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis, Delay Differential Equations in Bio-Populations, Tractable Model of Malignant Gliomas Immunotherapy with Discrete Time Delays, A dynamical model of tumour immunotherapy, Passing to the limit 2D–1D in a model for metastatic growth, Analysis of a stochastic tumor-immune model with regime switching and impulsive perturbations, A theoretical study of the response of vascular tumours to different types of chemotherapy, Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy, Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method, Mathematical modeling of tumor-immune competitive system, considering the role of time delay, A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth, Analysis of the Hopf bifurcation for the family of angiogenesis models, On the role of the objective in the optimization of compartmental models for biomedical therapies, The dynamical behaviors for a class of immunogenic tumor model with delay, Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers, Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors, Resonance of the epidemic threshold in a periodic environment, Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis, Mesoscopic and continuum modelling of angiogenesis, Stability of a mathematical model of tumour-induced angiogenesis, Optimisation of Cancer Drug Treatments Using Cell Population Dynamics, Tumor Development Under Combination Treatments with Anti-angiogenic Therapies, Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays, Qualitative analysis of tumor growth model under antiangiogenic therapy - choosing the effective operating point and design parameters for controller design, TUMOR-IMMUNE SYSTEM INTERACTION: MODELING THE TUMOR-STIMULATED PROLIFERATION OF EFFECTORS AND IMMUNOTHERAPY, Global stability and optimisation of a general impulsive biological control model, On optimal delivery of combination therapy for tumors, A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Bifurcation of nontrivial periodic solutions for a Beddington-DeAngelis interference model with impulsive biological control, Tumour growth and its treatment response delineate with mathematical models, Effect of treatment on the global dynamics of delayed pathological angiogenesis models, Periodic solutions for a model of tumor volume with anti-angiogenic periodic treatment



Cites Work