In particular community the rate of new cases of diabetes and the rate of new cases of flu during the monthe of january were precisely the same which disease would have the higher prevalence rate

Okay I am going to say first that this question is a little weird...new cases are usually measured by incidence where as prevalence would be the total number of cases. So to answer this particular question, one would only be able to answer it by assuming that there were no existing cases of flu or diabetes in January and then the new cases, which basically started at zero, equaled out to the same number in January. If that is true then they would be the same. Presumably, the Flu is a short term illness and Diabetes is not so it is more likely that Diabetes would have a higher prevalence rate...but again this is just an assumption since you have missing information from the question.

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