# Theoretical epidemiology and general mathematical investigations

First of all, let me say that I'am a mathematician working on mathematical physics. My wife was working on epidemiology on her master's and discussing with her I found the theme very interesting. When searching for "mathematical aspects of epidemiology" , I found only studies about mathematical modelling of specific diseases/infections by means of differential equations. On the other hand, since epidemiology involves data, it could also be related with data analysis and statistics. For data analysis we have topological data analysis, which is based on persistence homology, a very interesting topic (for me).

On the other hand, I feel (recall that I am stupid in this subject) that the basis of epidemiology is not too well mathematically formalized and it is precisely in this point that I am interested in. For example,

1. what is, formally speaking, an "epidemiological system"?
2. what is, formally speaking, an "epidemiological investigation"?
3. there is also a notion of emergence in epidemiology, but, what is, formally speaking, an emergence phenomena between epidemiological systems?
4. one time defined these, can we find some general results for them?

Of course, as maybe is clear, I am not interested in specific models and investigations on given concrete data. Indeed, I am interested in asking general/theoretic questions.

My first insight appeared when I working in this project, where I'm trying to develop a general theory for strong emergence phenomena between classical field theories.

Thanks and sorry if my questions are too vague.

• Interesting as it is, I would not call this a mathematics question. – kimchi lover Aug 27 '20 at 16:56
• I see. On the other hand, I believe that it has potential to be. – Math-Phys-Cat Group Aug 27 '20 at 17:08
• There are SE groups on medical sciences and on statistics, both of which seem more appropriate for questions about a branch of applied mathematics that hasn't been invented yet. – kimchi lover Aug 27 '20 at 17:39
• Ok.. Thank you. – Math-Phys-Cat Group Aug 28 '20 at 15:22
• I did not mean to belittle your question. But it is not (yet) a mathematics question. – kimchi lover Aug 28 '20 at 15:47