Dynamic ridesharing is a derivative of regular carpooling, which enables the formation of carpools on an as-needed basis, usually on very short notice the shared travel purpose also extends to a broad range of activities, beyond work or school. In this paper we propose a model to monitor the adoption of a dynamic ridesharing service, intended here as a mobile service that needs to achieve a critical mass to survive. Our theoretical model is inspired from the SIR model used in epidemiology to control the spread of an infectious virus. We test our model using real-data from two firms offering dynamic ridesharing services. Our model complements the view that innovative services evolve following an S-shaped curve, and it has practical relevance for managers and investors, who want to monitor and compare the evolution of competing firms in the field.