Download Number of people infected

Number of people infected
Number of people infected after exchange #4 if only one person is infected at the start
start
After Exchange #1
After Exchange #2
After Exchange #3
After Exchange #4
Least Possible Number of
People Infected
1
2
4
4
6
Greatest Possible Number of
People Infected
1
2
4
8
16
Assume that at the start of the activity that person A is infected and everybody else is
susceptible.
After Exchange #1: Possible number of people infected: 2
Greatest Possible Number Infected and Least Possible Number Infected: These numbers are the
same and each is calculated by the fact that the infected person, A, exchanges fluids with a
susceptible person, B, which causes 1 new infected person. At the end of exchange #1, the
greatest number infected is 1 + 1 = 2.
After Exchange #2: Possible number of people infected: 4
Greatest Possible Number Infected and Least Possible Number Infected: These numbers are the
same and each is calculated by the fact that the infected person, A and B, exchanges fluids with
a susceptible person, C and D respectively, which causes 2 new infected people. At the end of
exchange #2, the greatest number infected is 2 + 2 = 4.
After Exchange #3: Possible number of people infected: 4, 6, or 8
Greatest Possible Number Infected: This number is calculated by assuming that each of the four
infected people exchanges fluids with a susceptible person, which causes 4 new infected people.
At the end of exchange #3, the greatest number infected is 8.
Least Possible Number Infected: Since nobody knows who is and who isn’t infected, it is possible
that Person A exchanges fluids with Person D. However, since they are both already infected,
their exchange of fluid does not cause a new infection. It is equally possible that Person B
exchanges fluids with Person C. Again, since they are both already infected, their exchange of
fluid does not cause a new infection. At the end of exchange #3, the least number infected is 3 +
1+ 0 = 4.
After Exchange #4: Possible number of people infected: 6 – 16 even
Greatest Possible Number Infected: This number is calculated by assuming that each of the eight
infected people exchanges fluids with a susceptible person, which causes 8 new infected people.
At the end of exchange #4, the greatest number infected is 16
Least Possible Number Infected: If only four people were infected at the end of exchange #3,
then all four infected people must make contact with four susceptible people, leading to four new
infections and a total of eight infected people. However, it turns out that, instead of four people, if
six people were infected at the end of exchange #3, then it is possible that these six people can
exchange fluids amongst themselves without infecting any new susceptible people. Thus the
least number of infected people after exchange #4 is 6 people.