The project proposal should be roughly one page (single spaced, 1 inch margins). References may be included. In fact, I suggest you find at least two published papers related to the topic to get a feel for what has been done/what would be involved in modeling.
The purpose of the proposal is to clearly present a question regarding your application that you intend to answer using a mathematical model, and to describe why answering that question is important. For the proposal, consider that you are applying for funding/permission to pursue this research topic. As with many funding requests, your proposal will be peer-reviewed. You do not need to have identified the precise methods that you will employ (compare to Introduction section below), however you should try to describe at least what type of equation will be used in the model (e.g., difference vs. differential, ordinary vs. partial, linear vs. nonlinear, stochastic vs. deterministic, etc.). Lastly, please define all uncommon terms and concepts as if the reader is not an expert in the application, but has a mathematical background.