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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.

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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.

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    Say I want to write a paper that describes this field and goes into detail with some common concepts that are typically in most papers. How would I go by this without simply regurgitating a bunch of information from different papers? Say I wanted to put my own original twist to it.
    – H5159
    Dec 13, 2015 at 2:03
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    @Frumpy sounds like you're talking about writing review paper, not original research (developing a new model.) That's a completely different question.
    – ff524
    Dec 13, 2015 at 2:05
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    @Frumpy Research papers you see in journals are presenting novel information. Maybe they took an existing model or algorithm, and they made it more accurate, or more efficient. Maybe they presented a way a phenomenon acts that wasn't well-understood before. The point is that it's a new, or unexpected approach to understanding the field. You will regurgitate some info to show where the field is at in respect, but therein the experimental design, results and interpretation are yours.
    – CKM
    Dec 13, 2015 at 2:11
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    @Frumpy Good (publishable) review papers are also very time consuming and difficult to write, especially if you don't have a lot of experience in the field. Honestly, if you're looking to write a paper (that's publishable in a non-junk venue) from scratch in a month, it's not realistic. If you want to do this as a useful exercise for yourself (not to publish) it'd probably be a valuable thing for you to do, if you hope to do research in this field in the future.
    – ff524
    Dec 13, 2015 at 2:17
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    @Frumpy The best way to gain experience is to find an advisor to help guide that experience. Otherwise you are likely to waste a lot of time duplicating things that are already done by others (that you haven't found because they're called something else by the experts and you don't know the right search terms), or on ideas that aren't useful (which you haven't realized because you don't know that all the experts already considered and rejected this idea), etc.
    – ff524
    Dec 13, 2015 at 2:28

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