Probability of Ending up Sick after 3 rounds

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Start with two people "sick" in a group with a total of 100. In round 1, each person shares with another person. The two sick people can share with anyone. If they share with each other then the number of sick people remains at 2. They continue this for 2 more rounds. If person A had already shared with person B then they can't share again in future rounds. If person A shared with B and person C with D, then person B can share with person D. If two sick people share with each other than they both remain sick. At the end of round three what is the probability that 6 people are sick? 8 People? 10? and so forth until 16.