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

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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).

Keywords

Chemotherapy
Nonautonomous logistic growth
Periodic orbit
Stability analysis

UN SDGs

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

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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.

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KW - Nonautonomous logistic growth

KW - Periodic orbit

KW - Stability analysis

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

Abstract

Bibliographical note

Keywords

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