While host-parasite interactions are ubiquitous, the large-scale consequences of parasite infections are mainly driven by the spatial context. One trait of pivotal importance for the eco-evolutionary dynamics of such metapopulations is the spatial behaviour of hosts, that is, their dispersal. It is well established that dispersal is not a random process, rather dispersal is informed and may depend on internal and external factors. In host-parasite metapopulations, dispersal may be a function of a host's infection state, but also of the local context, such as host density or parasite prevalence. Using a dynamical host-parasite metapopulation model of a parasite that reduces host fecundity (sterilizing parasite), we explore whether host dispersal evolves to be state-and context-dependent and what shapes the evolutionarily stable dispersal reaction norms have. We show that state-dependent dispersal readily evolves in the sense that hosts disperse more when infected, except when infected hosts pay significantly higher dispersal costs. This dispersal bias evolves due to kin selection, which is consistent with previous studies. Most importantly, we show that prevalence-dependent dispersal evolves, especially when virulence is high and epidemiological dynamics have predictable signatures. The observed evolutionary outcome, a negatively prevalence-dependent dispersal reaction norm for susceptible hosts at high virulence, seems counter-intuitive at first. However, our results can be readily explained by the emergent epidemiological dynamics, especially their spatial and temporal correlation patterns. Finally, we show that context-dependency in dispersal may rely on both, prevalence, and host density cues. Our work provides new insights into the evolution of complex dispersal phenotypes in host-parasite metapopulations as well as on feedbacks with epidemiological dynamics.