Are there different sorts of infections that elderly people may suffer for 2 wks without an acute decline in physical symptoms? if so, examples please

Yes : In general terms a cold or other virus might. Also old people may present with significant infections without much in the way of physical symptoms. Eg a pneumonia or a urinary infection they may just appear a bit more muddled/confused than usual or a little off their food etc. also some infections like glandular fever have long incubation periods before they manifest.

Elderly patients: rarely present with typical disease symptoms presentations and this is why we use a high index of suspicion, since they may "appear fine", or somewhat slowed, but not flagrantly ill. A medical exam is necessary.

I'm not sure about: my colleagues, but I don't understand exactly what you are asking. In any case if you think an elderly person has an infection, it's best not to wait until they have an obvious decline in their general health before getting them medical care. Skin infections and urinary tract infections may be the most common but any infection can be dangerous to a frail, elderly person.