Why do some exotic species thrive so successfully once they have been introduced to a new environment? One of the reasons most frequently called upon is the enemy release hypothesis, which explains the inordinate success of introduced species by the lack of pressure from co-evolved natural enemies. In this talk, I consider the situation that the new environment changes in the sense that it does not remain free of natural enemies. More specifically, infectious diseases can follow their host and alter the fate of invasion. In particular, this may lead to a rather spontaneous invasion crash ("Now you see them, now you don't"). The mathematical models employed are reaction-diffusion systems with the feature of bistability. The results bear implications for potential biological control methods of invasive pest species.