Qualitative analysis of an integro-differential equation model of periodic chemotherapy

Harsh Vardhan Jain; Helen M. Byrne

doi:10.1016/j.aml.2012.04.024

Qualitative analysis of an integro-differential equation model of periodic chemotherapy

Harsh Vardhan Jain
, Helen M. Byrne

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

11 Scopus citations

Abstract

An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.

Original language	English (US)
Pages (from-to)	2132-2136
Number of pages	5
Journal	Applied Mathematics Letters
Volume	25
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2012.04.024
State	Published - Dec 2012
Externally published	Yes

Bibliographical note

Funding Information:
The authors thank Profs Avner Friedman and Marty Golubitsky and Drs Rachel Leander and Yunjiao Wang for many helpful discussions. This research has been supported in part by the MBI and the NSF (grant DMS 0931642 ). This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Chemotherapy
Nonautonomous logistic growth
Periodic orbit
Stability analysis

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10.1016/j.aml.2012.04.024

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title = "Qualitative analysis of an integro-differential equation model of periodic chemotherapy",

abstract = "An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.",

keywords = "Chemotherapy, Nonautonomous logistic growth, Periodic orbit, Stability analysis",

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note = "Funding Information: The authors thank Profs Avner Friedman and Marty Golubitsky and Drs Rachel Leander and Yunjiao Wang for many helpful discussions. This research has been supported in part by the MBI and the NSF (grant DMS 0931642 ). This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).",

year = "2012",

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doi = "10.1016/j.aml.2012.04.024",

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AU - Jain, Harsh Vardhan

AU - Byrne, Helen M.

N1 - Funding Information: The authors thank Profs Avner Friedman and Marty Golubitsky and Drs Rachel Leander and Yunjiao Wang for many helpful discussions. This research has been supported in part by the MBI and the NSF (grant DMS 0931642 ). This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).

PY - 2012/12

Y1 - 2012/12

N2 - An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.

AB - An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.

KW - Chemotherapy

KW - Nonautonomous logistic growth

KW - Periodic orbit

KW - Stability analysis

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SP - 2132

EP - 2136

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 12

ER -

Qualitative analysis of an integro-differential equation model of periodic chemotherapy

Abstract

Bibliographical note

UN SDGs

Keywords

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