Epidemiological models for multi-host pathogen systems often classify individuals taxonomically and use species-specific parameter values, but in species-rich communities, that approach may require intractably many parameters. Trait-based epidemiological models offer a potential solution, but have not accounted for within-species trait variation or between-species trait overlap. Here, we propose and study trait-based models with host and vector communities represented as trait distributions without regard to species identity. To illustrate this approach, we develop SIS models for disease spread in plant-pollinator networks with continuous trait distributions. We model trait-dependent contact rates in two common scenarios: nested networks, and specialized plant-pollinator interactions based on trait matching. We find that disease spread in plant-pollinator networks is impacted the most by selective pollinators, universally attractive flowers, and co-specialized plant-pollinator pairs. When extreme pollinator traits are rare, pollinators with common traits are most important for disease spread, whereas when extreme flower traits are rare, flowers with uncommon traits impact disease spread the most. Greater nestedness and specialization both typically promote disease persistence. Given recent pollinator declines caused in part by pathogens, we discuss how trait-based models could inform conservation strategies for wild and managed pollinators. Furthermore, while we have applied our model to pollinators and pathogens, its framework is general and can be transferred to any kind of species interactions, in any community.