help me come up with a good project idea and develop real data, define parameters, define, set up and solve differential equations and interpret results. see project instructions below.

The project for this term will be an independent research project/experiment applying differential equations. You may likely choose a topic that applies concepts and methods explained in class but that goes beyond the topics and methods covered in class or you may need to apply topics not covered until the very end of the course. You and your group will choose a scenario that can be represented as a differential equation such as a cascading salt-vat scenario (ideas permeating in a group of people, money distributed in an economy, deadly or non-deadly mutating or non-mutating virus permeating a society, etc.), spring-mass scenario (conservative and liberal discourse on a topic, emotional progress through tragedy, regaining financial stability after debt, etc.) or any topic that begins with the derivative defined as a set of influences (how one changes one's mind, orbits around a star or two stars, bungee jumping, bloodalcohol level, predator-prey scenarios, etc.). Define your parameters, create your equation(s), solve for the generating equations and interpret your results| - it is possible that you may choose a topic that cannot be solved using equations, but could be approximated