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The risk of antibiotic resistance evolution in parasites is a major problem for public health. Identifying factors which promote antibiotic resistance evolution is thus a priority in evolutionary medicine. The rate at which new mutations enter the parasite population is one important predictor; however, mutation rate is not necessarily a fixed quantity, as is often assumed, but can itself evolve. Here we explore the possible impacts of mutation rate evolution on the fate of a disease circulating in a host population, which is being treated with drugs, the use of which varies over time. Using an evolutionary rescue framework, we find that mutation rate evolution provides a dramatic increase in the probability that a parasite population survives treatment in only a limited region, while providing little or no advantage in other regions. Both epidemiological features, such as the virulence of infection, and population genetic parameters, such as recombination rate, play important roles in determining the probability of evolutionary rescue and whether mutation rate evolution enhances the probability of evolutionary rescue or not. While efforts to curtail mutation rate evolution in parasites may be worthwhile under some circumstances, our results suggest that this need not always be the case., (Copyright © 2017 Elsevier Inc. All rights reserved.)