| 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 a compartmental system of ODEs. The simplicity of our model allows us to obtain analytic results for resistance to any number of drugs. Our main result is 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. This result seems to contradict some results in the literature, and a detailed discussion is provided. |
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