An elementary approach to modeling drug resistance in cancer

Abstract

Resistance to drugs has been an ongoing obstacle to a successfultreatment of many diseases. In this work we consider the problem ofdrug resistance in cancer, focusing on random genetic point mutations.Most previous works on mathematical models of such drug resistancehave been based on stochastic methods. In contrast,our approach is based on an elementary, compartmental system of ordinarydifferential equations.We use our very simple approach to derive resultson 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 forresistance to any number of drugs.In particular, we show that the amountof resistance generated before the start of the treatment, and present at some given time afterward, always depends onthe turnover rate, no matter how many drugs are simultaneously used inthe treatment.

Keywords

• ordinary differential equations
• cancer
• stochastic methods.
• drugresistance