On the mathematical modelling of tumor-induced angiogenesis

DOI10.3934/mbe.2017004zbMath1352.92076OpenAlexW2530100207WikidataQ50544162 ScholiaQ50544162MaRDI QIDQ335241

Luis L. Bonilla, Vincenzo Capasso, Filippo Terragni, Mariano Alvaro, Manuel Carretero

Publication date: 2 November 2016

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

Full work available at URL: https://doi.org/10.3934/mbe.2017004

zbMATH Keywords

stochastic differential equationsensemble averagegrowth processeshybrid modelsmean field approximationchaos propagationbirth-and-death processestumor-induced angiogenesis

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of branching processes (60J85) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Medical applications (general) (92C50) Applications of stochastic analysis (to PDEs, etc.) (60H30) Random measures (60G57) Stochastic particle methods (65C35)

Related Items (4)

Integrodifference master equation describing actively growing blood vessels in angiogenesis ⋮ Large and moderate deviations for kernel-type estimators of the mean density of Boolean models ⋮ The mathematical modeling of cancer growth and angiogenesis by an individual based interacting system ⋮ On the mean field approximation of a stochastic model of tumour-induced angiogenesis

Cites Work

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• Lattice and non-lattice models of tumour angiogenesis
• Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis
• A deterministic model of growth factor-induced angiogenesis
• On the approximation of mean densities of random closed sets
• Stochastic modelling of tumour-induced angiogenesis
• On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
• Point processes and queues. Martingale dynamics
• Continuous and discrete mathematical models of tumor-induced angiogenesis
• An interacting particle system modelling aggregation behavior: from individuals to populations
• Mathematical modeling of tumor-induced angiogenesis
• Invasion and adaptive evolution for individual-based spatially structured populations
• On an aggregation model with long and short range interactions
• Mathematical modelling of the influence of blood rheological properties upon adaptative tu\-mour-induced angiogenesis
• Mesoscale Averaging of Nucleation and Growth Models
• On the Geometric Densities of Random Closed Sets
• The role of stochasticity in a model of retinal angiogenesis
• Multiscale Angiogenesis Modeling Using Mixed Finite Element Methods
• An introduction to continuous-time stochastic processes. Theory, models, and applications to finance, biology, and medicine

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