An elementary approach to modeling drug resistance in cancer

Cristian Tomasetti; Doron Levy; Cristian Tomasetti; Doron Levy

doi:10.3934/mbe.2010.7.905

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 4: 905-918. doi: 10.3934/mbe.2010.7.905

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An elementary approach to modeling drug resistance in cancer

1.
Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742

Received: 01 April 2010 Accepted: 29 June 2018 Published: 01 October 2010
MSC : Primary: 92B05; Secondary: 34A30.

Resistance to drugs has been an ongoing obstacle to a successful treatment of many diseases. In this work we consider the problem of drug resistance in cancer, focusing on random genetic point mutations. Most previous works on mathematical models of such drug resistance have been based on stochastic methods. In contrast, our approach is based on an elementary, compartmental system of ordinary differential equations. We use our very simple approach to derive results on drug resistance that are comparable to those that were previously obtained using much more complex mathematical techniques. The simplicity of our model allows us to obtain analytic results for resistance to any number of drugs. In particular, we show that the amount of resistance generated before the start of the treatment, and present at some given time afterward, always depends on the turnover rate, no matter how many drugs are simultaneously used in the treatment.

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Citation: Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer[J]. Mathematical Biosciences and Engineering, 2010, 7(4): 905-918. doi: 10.3934/mbe.2010.7.905

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Abstract

Resistance to drugs has been an ongoing obstacle to a successful treatment of many diseases. In this work we consider the problem of drug resistance in cancer, focusing on random genetic point mutations. Most previous works on mathematical models of such drug resistance have been based on stochastic methods. In contrast, our approach is based on an elementary, compartmental system of ordinary differential equations. We use our very simple approach to derive results on drug resistance that are comparable to those that were previously obtained using much more complex mathematical techniques. The simplicity of our model allows us to obtain analytic results for resistance to any number of drugs. In particular, we show that the amount of resistance generated before the start of the treatment, and present at some given time afterward, always depends on the turnover rate, no matter how many drugs are simultaneously used in the treatment.

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