Strain structure is of fundamental importance in the underlying dynamics of a number of pathogens. However, previous models have been too complex to accommodate many strains. This paper offers a solution to this problem, in the form of a simple model that is capable of capturing the dynamics of a large number of antigenic types that interact via host cross-immunity. We derive the structure of the model, which can manage the complexity of many strains by using a status-based formulation, assuming polarized immunity and cross-immunity act to reduced transmission probability. We then apply the model to address basic questions in strain dynamics, focusing particularly on the interpandemic dynamics of influenza. This model shows that strains have a tendency to "cluster." For a long infectious period, relative to host lifetime, clusters may coexist. By contrast, a short infectious period leads to a single dominant cluster at any given time. We show how the speed of cluster replacement depends on the specificity of cross-immunity and on the underlying pathogen mutation rate.