Abstract Models of particular epidemiological systems can rapidly become complicated by biological detail which can obscure their essential features and behaviour. In general, we wish to retain only those components and processes that contribute to the dynamics of the system. In this paper, we apply asymptotic techniques to an SEI-type model with primary and secondary infection in order to reduce it to a much simpler form. This allows the identification of parameter groupings discriminating between regions of contrasting dynamics and leads to simple approximations for the model’s transient behaviour. These can be used to follow the evolution of the developing infection process. The techniques examined in this paper will be applicable to a large number of similar models.