It's not clear what type of model you were thinking of: a transmission model of the spread in a population, a mechanistic model within a human host? Also, UTIs can be caused by quite different types of bacteria, although most are enteric, so maybe best to model only the most prevalent one, which would be uropathogenic E. coli. 

Hi Stephen,

Interesting problem!

I can think of a statistical model where if you input variables A,B and C to the system, the system behaves normally, that is, there is no infection, but if you input variables D,E and F (say, alcohol, salty food, exposure to certain bacteria, etc) then the system behaves abnormally.

Statistical analysis of hospital databases would allow you calibrate the model: defining, for instance, the number and type of variables which produce abnormal conditions. A neural network would capture the highly non-linear nature of the relationship between input and output, i.e. to what input corresponds what degree of abnormality.

My 15 cents!

Hope it helps,

Augusto

 Dear stephen:

In my opinion you should concrete the question: which mathematical model are you searchirng for?: an epidemiological model based on the propagation of an outbreak of UTI among a determined populationd population or a risk factor model based on the determination of variables which influence the appearance of a UTI.