Effect of treatment on the global dynamics of delayed pathological angiogenesis models

Leonid Berezansky; Elena Braverman; Lev Idels

doi:10.1016/j.jtbi.2014.08.012

Effect of treatment on the global dynamics of delayed pathological angiogenesis models

Leonid Berezansky
, Elena Braverman
, Lev Idels

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.

Original language	English
Pages (from-to)	13-21
Number of pages	9
Journal	Journal of Theoretical Biology
Volume	363
DOIs	https://doi.org/10.1016/j.jtbi.2014.08.012
State	Published - 21 Dec 2014

Keywords

Angiogenesis
Global stability
Impulsive treatment
Systems of nonlinear nonautonomous delay differential equations

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.jtbi.2014.08.012

Cite this

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title = "Effect of treatment on the global dynamics of delayed pathological angiogenesis models",

abstract = "For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.",

keywords = "Angiogenesis, Global stability, Impulsive treatment, Systems of nonlinear nonautonomous delay differential equations",

author = "Leonid Berezansky and Elena Braverman and Lev Idels",

note = "Funding Information: L. Berezansky is partially supported by the Israeli Ministry of Absorption, Braverman is partially supported by NSERC DG Research Grant- 2010 (Grant no. 261351), Idels is partially supported by a grant from VIU. The authors are very grateful to the anonymous referee for useful remarks and comments.",

year = "2014",

month = dec,

day = "21",

doi = "10.1016/j.jtbi.2014.08.012",

language = "English",

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journal = "Journal of Theoretical Biology",

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TY - JOUR

T1 - Effect of treatment on the global dynamics of delayed pathological angiogenesis models

AU - Berezansky, Leonid

AU - Braverman, Elena

AU - Idels, Lev

N1 - Funding Information: L. Berezansky is partially supported by the Israeli Ministry of Absorption, Braverman is partially supported by NSERC DG Research Grant- 2010 (Grant no. 261351), Idels is partially supported by a grant from VIU. The authors are very grateful to the anonymous referee for useful remarks and comments.

PY - 2014/12/21

Y1 - 2014/12/21

N2 - For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.

AB - For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.

KW - Angiogenesis

KW - Global stability

KW - Impulsive treatment

KW - Systems of nonlinear nonautonomous delay differential equations

UR - https://www.scopus.com/pages/publications/84906489606

U2 - 10.1016/j.jtbi.2014.08.012

DO - 10.1016/j.jtbi.2014.08.012

M3 - Article

AN - SCOPUS:84906489606

SN - 0022-5193

VL - 363

SP - 13

EP - 21

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

ER -

Effect of treatment on the global dynamics of delayed pathological angiogenesis models

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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