The probability of treatment induced drug resistance.

We propose a discrete time branching process to model the appearance of drug resistance under treatment. Under our assumptions at every discrete time a pathogen may die with probability 1-p or divide in two with probability p. Each newborn pathogen is drug resistant with probability mu. We start with N drug sensitive pathogens and with no drug resistant pathogens. We declare the treatment successful if all pathogens are eradicated before drug resistance appears. The model predicts that success is possible only if p<1/2. Even in this case the probability of success decreases exponentially with the parameter m=muN. In particular, even with a very potent drug (i.e. p very small) drug resistance is likely if m is large.