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Population epidemiological models where hosts can be infected sequentially by different strains have the potential to help us understand many important diseases. Researchers have in recent years started to develop and use such models, but the extra layer of complexity from multiple strains brings with it many technical challenges. It is therefore hard to build models which have realistic assumptions yet are tractable. Here we outline some of the main challenges in this area. First we begin with the fundamental question of how to translate from complex small-scale dynamics within a host to useful population models. Next we consider the nature of so-called “strain space”. We describe two key types of host heterogeneities, and explain how models could help generate a better understanding of their effects. Finally, for diseases with many strains, we consider the challenge of modelling how immunity accumulates over multiple exposures. [ABSTRACT FROM AUTHOR]