I proposed this in my 'bio warfare' section.
Pandemics can be created through strategic weapons and are harder to suppress if higher quality.
Pandemics require quarantining from military units - so it incapacitates some of your mobile land defense units (and supply units if they need to work for a long enough time to deplete their resources); if you don't have any, then a message appears saying that you need to create some before conducting a relief effort - and some number of doctors/nurses/senior doctors are needed for the relief effort. If you have to pull doctors/etc. out of hospitals, then you need to pay more on the relief effort.
As for 'vaccination centers' - I'm thinking instead 'quarantine hospitals', which are like special clinics in that they need to be converted from regular hospitals (any number can be converted at any time though, and it's immediate - but there's also a fee associated). Quarantine hospitals are an easier way to recruit doctors/nurses/etc. to work against a pandemic than actually assigning them through the relief effort - but this also knocks off the health index, obviously. Outside of a pandemic, only 5 or so can be converted per month.
So my suggestion is potentially more punishing - also bio warfare creates even worse pandemics than nature, if properly delivered (standard procs). The risk of pandemic only appears once you go over the regular population cap (60 mil I think?).