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.
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.