Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay

R. A. Everett; J. D. Nagy; Yang Kuang

doi:10.1007/s10884-015-9498-y

Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay

R. A. Everett, J. D. Nagy, Yang Kuang

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

5 Scopus citations

Abstract

We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop’s cell quota model, a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including proving positivity of the solutions so that they are biologically meaningful, as well as discussing local and global stability. The mathematical model can be employed to fit both on-treatment and off-treatment preclinical data using the same biologically relevant parameters. We also state an open mathematical question.

Original language	English (US)
Journal	Journal of Dynamics and Differential Equations
DOIs	https://doi.org/10.1007/s10884-015-9498-y
State	Accepted/In press - Sep 30 2015

Keywords

Data validation
Delay equation
Droop model
Ovarian tumor model
Stability

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s10884-015-9498-y

Cite this

@article{834bc88c9ce6455e96c581b65b7c1dc2,

title = "Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay",

abstract = "We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop{\textquoteright}s cell quota model, a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including proving positivity of the solutions so that they are biologically meaningful, as well as discussing local and global stability. The mathematical model can be employed to fit both on-treatment and off-treatment preclinical data using the same biologically relevant parameters. We also state an open mathematical question.",

keywords = "Data validation, Delay equation, Droop model, Ovarian tumor model, Stability",

author = "Everett, {R. A.} and Nagy, {J. D.} and Yang Kuang",

year = "2015",

month = sep,

day = "30",

doi = "10.1007/s10884-015-9498-y",

language = "English (US)",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

}

TY - JOUR

T1 - Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay

AU - Everett, R. A.

AU - Nagy, J. D.

AU - Kuang, Yang

PY - 2015/9/30

Y1 - 2015/9/30

N2 - We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop’s cell quota model, a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including proving positivity of the solutions so that they are biologically meaningful, as well as discussing local and global stability. The mathematical model can be employed to fit both on-treatment and off-treatment preclinical data using the same biologically relevant parameters. We also state an open mathematical question.

AB - We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop’s cell quota model, a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including proving positivity of the solutions so that they are biologically meaningful, as well as discussing local and global stability. The mathematical model can be employed to fit both on-treatment and off-treatment preclinical data using the same biologically relevant parameters. We also state an open mathematical question.

KW - Data validation

KW - Delay equation

KW - Droop model

KW - Ovarian tumor model

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84944707457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944707457&partnerID=8YFLogxK

U2 - 10.1007/s10884-015-9498-y

DO - 10.1007/s10884-015-9498-y

M3 - Article

AN - SCOPUS:84944707457

SN - 1040-7294

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

ER -

Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this