When I've been away from my computer and want to check on my villages, the first thing I do (after deciding on the event, if needed) is go to the Details screen and quickly scroll through the population. That will show me any villagers who are sick or in the rare instances, those whose health bars are critical.

After curing each villager (dragging them to the "clinic" area and grabbing a kid from the garden), I'll watch to make sure that all of the dead are buried.

Then I check on any other "maintenance" that is needed (like how many breeders I have and making sure any teenagers have something to do) and then go on to the next game.