There is a group of people, some of whom are friends with one another (all friendships are mutual). Then one day, one of them gets sick. The sickness obeys the following rules:
On day 1, one person is sick with the virus, and nobody has immunity.
Illness lasts exactly one day.
Next day the recovered patient has immunity for a day.
If a person is sick, all of his friends who are not sick that day go to visit him in bed. They get sick next day, unless they were immune when they visited him.
Prove that the pandemics will end in a finite amount of time.
(No, this disease is not COVID. Call it mathitis)