The evidence produced in mathematical models plays a key role in shaping policy decisions in pandemics. A key question is therefore how well pandemic models relate to their implementation contexts. Drawing on the cases of Ebola and influenza, we map how sociological and anthropological research contributes in the modelling of pandemics to consider lessons for COVID-19. We show how models detach from their implementation contexts through their connections with global narratives of pandemic response, and how sociological and anthropological research can help to locate models differently. This potentiates multiple models of pandemic response attuned to their emerging situations in an iterative and adaptive science. We propose a more open approach to the modelling of pandemics which envisages the model as an intervention of deliberation in situations of evolving uncertainty. This challenges the ‘business-as-usual’ of evidence-based approaches in global health by accentuating all science, within and beyond pandemics, as ‘emergent’ and ‘adaptive’.