How are disease vectors for non-lethal communicable diseases found?

There are loads of popular literature/fact/movies dealing with the communication of deadly diseases, such as an outbreak of Ebola. But how do the health authorities deal with plotting disease vectors for non-lethal outbreaks? For example, the States is experiencing its worst outbreak of mumps since regular vaccination was started. Can the health authorities trace this outbreak back to a patient-zero? How do they identify when/where (and in some cases how) the disease was spread? Or, in fact, if imminent great loss of life is not a concern, do they even bother? Is it more or less difficult than with lethal disease? Are there different considerations? (It seems to me that the transmission would possibly be even faster and/or more widespread, as with the usual winter flu . . .)