The Red Queen hypothesis posits a promising way to explain the widespread existence of sexual reproduction despite the cost of producing males. The essence of the hypothesis is that coevolutionary interactions between hosts and parasites select for the genetic diversification of offspring via cross-fertilization. Here, I relax a common assumption of many Red Queen models that each host is exposed to one parasite. Instead, I assume that the number of propagules encountered by each host depends on the number of infected hosts in the previous generation, which leads to additional complexities. The results suggest that epidemiological feedbacks, combined with frequency-dependent selection, could lead to the long-term persistence of sex under biologically reasonable conditions.