More people than ever are paying attention to philosophical questions about epidemiological models, including their susceptibility to the influence of social and ethical values, sufficiency to inform policy decisions under certain conditions, and even their fundamental nature. One important question pertains to the purposes of epidemiological models, for example, are COVID-19 models for 'prediction' or 'projection'? Are they adequate for making causal inferences? Is one of their goals, or virtues, to change individual responses to the pandemic? In this essay, we offer our perspective on these questions and place them in the context of other recent philosophical arguments about epidemiological models. We argue that clarifying the intended purpose of a model, and assessing its adequacy for that purpose, are moral-epistemic duties, responsibilities which pertain to knowledge but have moral significance nonetheless. This moral significance, we argue, stems from the inherent value-ladenness of models, along with the potential for models to be used in political decision making in ways that conflict with liberal values and which could lead to downstream harms. Increasing conversation about the moral significance of modelling, we argue, could help us to resist further eroding our standards of democratic scrutiny in the COVID-19 era.