Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.