We characterise the evolutionary dynamics of influenza infection described by viral sequence data collected from two challenge studies conducted in human hosts. Viral sequence data were collected at regular intervals from infected hosts. Changes in the sequence data observed across time show that the within-host evolution of the virus was driven by the reversion of variants acquired during previous passaging of the virus. Treatment of some patients with oseltamivir on the first day of infection did not lead to the emergence of drug resistance variants in patients. Using an evolutionary model, we inferred the effective rate of reassortment between viral segments, measuring the extent to which randomly chosen viruses within the host exchange genetic material. We find strong evidence that the rate of effective reassortment is low, such that genetic associations between polymorphic loci in different segments are preserved during the course of an infection in a manner not compatible with epistasis. Combining our evidence with that of previous studies we suggest that spatial heterogeneity in the viral population may reduce the extent to which reassortment is observed. Our results do not contradict previous findings of high rates of viral reassortment in vitro and in small animal studies, but indicate that in human hosts the effective rate of reassortment may be substantially more limited.