To date the vast majority of the work into disease transmission on networks has focused on static networks where all links are of equal strength and, therefore, associated with the same basic rate of transmission. However, it is clear that contact networks change over time (both on the short-time scale of who we meet each day, and on the longer time-scale of who our main work and social contacts are), and that links have different weights (such that some contacts are much more likely to lead to the transmission of infection than others). While the simulation of infection on such weighted time-varying networks is feasible, it is unclear how the existing sets of network properties or the existing literature of analytical approaches can be extended to such higher-dimensional networks.