Where can I find data on which to base mathematical modeling with differential equaitons? Where can I find data and models on which to base mathematical modeling with differential equations? We are building a community of colleagues interested in using modeling to motivate teaching differential equations and we seek good sources of data and models to offer colleagues. Any leads, examples, pointers, engagements, etc. would be appreciated. Brian Winkel, Director SIMIODE at www.simiode.org.  Thank you.

I absolutely love your idea! From my humble experience of collaboration with researchers from multiple fields, I would suggest that you let the students choose a topic first.
For example, let say the topic is to model the spreading of Ebola using an SIR system of equation. Then a good source of data is WHO (World Health Organization) Link. Better yet, the data has spatial component and thus the model can be extended to a PDE.
Another example, this time let's pick mathematical modeling in medicine. There are a few ways to obtain good data, but the fastest method is probably through direct collaboration with previous authors who have used/obtained the data. To find these authors, a google.scholar search is probably sufficient. I would suggest a recent (2016) text by Yang Kuang on mathematical oncology, Link. The text contains a broad survey of the field with great biological details, mathematical analysis and matlab code.
In general, for any topic, there is probably a credible journal with good data (but may require contacting the authors for permission to use them). For example, data for various aspects of a marine fish biological system can be found in Theoretical Ecology.
In the case that these are not available, I would suggest obtaining data through collaboration with current scientists/students who are working in labs within their respective university. Although this has the risk of obtaining less than great data, it gives several benefits such as the experience of collaboration that a good majority of math students lacks. In fact for a simple physical project, it would be fun for the students themselves to carry out experiments under supervision to collect their own data too!!
I hope this helps! Good luck! :)
