Some years ago, my grandfather worked for an auto manufacturer. Much of his job could best be described as the "drunk wrangler." Absenteeism was so high on Mondays that his job was to go out and roust enough employees out of bed so they could start the assembly line.
The problem isn't illness, it's laziness -- and union contracts.
German automakers actually have a saying along the lines of, "Never buy a Monday Car."