Model for tumour growth with treatment by continuous and pulsed chemotherapy

Bio Systems
F S BorgesC Grebogi

Abstract

In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the parameters according to experimental results and vary some parameters relevant to the treatment of cancer. We find that our model exhibits a dynamical behaviour associated with the suppression of cancer cells, when either continuous or pulsed chemotherapy is applied according to clinical protocols, for a large range of relevant parameters. When the chemotherapy is successful, the predation coefficient of the chemotherapic agent acting on cancer cells varies with the infusion rate of chemotherapy according to an inverse relation. Finally, our model was able to reproduce the experimental results obtained by Michor and collaborators [Nature 435 (2005) 1267] about the exponential decline of cancer cells when patients are treated with the drug glivec.

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Citations

Mar 22, 2016·Computational and Mathematical Methods in Medicine·Liuyong PangZhong Zhao
Jan 18, 2015·Journal of Theoretical Biology·Kelly C IaroszSergio R Lopes
Feb 1, 2014·Mathematical Biosciences·Hermane Mambili-MamboundouJoseph Malinzi
Jan 25, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Hai-Peng RenCelso Grebogi
Oct 6, 2020·Frontiers in Physiology·Paulo R ProtacheviczJürgen Kurths
Mar 20, 2021·Bulletin of Mathematical Biology·Katherine Owens, Ivana Bozic

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