Finding original research ideas/topics as an undergraduate student I am currently an undergraduate student majoring in mathematics and biology. My plan is to combine both of these fields with the hope of somehow working with modeling infectious diseases through the use of differential equations and other methods. 

I recently took a course in mathematical modeling and an independent study on modeling infectious diseases. I worked with the SI, SIS, SIR and other models. The main method was using differential equations to model the diseases. I've worked with very simple models that were logistic, to more complicated models such as the Zombie model. 

This field really interest me and I would like to work on some sort of topic that isn't well discussed or well known. Maybe even create my own model. However I don't particularly know where to start. How would I go by finding some sort starting point? Any help in the right direction would be appreciated. I am on winter break and I have a month of free time. I'd like to use this time to do some research and write a paper on it. Something that I may possibly use in the future.
To develop something that is both (1) new and (2) meaningful, you'd have to start by reading a lot of published research to find out what is already out there. After reading widely, you'd start to get a sense for what the trends are in the field, and possibly start to see some gaps that point to open research problems. You'd also start to see what you'd be expected to do and say in a similar paper, i.e. the standards and conventions in the field, what kind of contributions a new model is expected to make, etc.

This is very difficult and time consuming for someone working alone without a lot of experience in the field. (It would definitely take more than a month!) The best "shortcut" is to find one or more advisors (perhaps the advisor from your independent study?) who can help point you in a promising direction, and give you feedback on your work.