Since influenza in humans is a major public health threat, the understanding of its dynamics and evolution, and improved prediction of its epidemics are important aims. Underlying its multi-strain structure is the evolutionary process of antigenic drift whereby epitope mutations give mutant virions a selective advantage. While there is substantial understanding of the molecular mechanisms of antigenic drift, until now there has been no quantitative analysis of this process at the population level. The aim of this study is to develop a predictive model that is of a modest-enough structure to be fitted to time series data on weekly flu incidence. We observe that the rate of antigenic drift is highly non-uniform and identify several years where there have been antigenic surges where a new strain substantially increases infective pressure. The SIR-S approach adopted here can also be shown to improve forecasting in comparison to conventional methods.