Hi there,
You may not have gotten a response to this since you've placed the message in the MD/PhD forum. 😉
There are tons of MPH or M.Sc. Epidemiology programs out there. As to what they do on a daily basis, do you mean the students or one who works in the field, post-degree?
As to the stability of the career and the pay, it depends on which type of job you choose. Someone with this type of training alone could work in a public health unit as an epidemiologist and (here in Canada at least) be paid ~$60-75K per year. Alternatively, you could jump into a mid-level private sector position within a pharmaceutical firm and pull in a little more than that. I'd say both careers are fairly stable, given the more contemporary fear of outbreaks and increasing demand for drugs, respectively.
Cheers,
Kirsteen