There is a bunch of individuals, a few of whom are mates with each other (all friendships are mutual). Then in the future, one among them will get sick. The illness obeys the next guidelines:

• On day 1, one individual is sick with the virus, and no person has immunity.

• Illness lasts precisely in the future.

• Next day the recovered affected person has immunity for a day.

• If an individual is sick, all of his mates who are usually not sick that day go to go to him in mattress. They get sick subsequent day, until they had been immune after they visited him.

Prove that the pandemics will finish in a finite period of time.

(No, this illness isn’t COVID. Call it mathitis)