Hermit Model

1. Use a six-sided die where each side represents a hermit.

2. Roll the die to see which hermit gets the disease.

3. Roll the die again to see which hermit is visited and gets the disease.

4. Continue rolling until an immune hermit (one of the numbers that has already been rolled) is visited.
   NOTE:If the same number is rolled one after the other, ignore the second roll, since these hermits do not visit themselves.

5. Count how many different numbers were rolled (how many hermits got the disease).

6. Repeat steps 2-5 many times.

7. Average the number of hermits who got infected per outbreak.

There are many other possible ways to model this problem. Can you think of any?

How could you model an island with 4 hermits? 10 hermits? 52 hermits?

Sometimes it can be handy to refer back to the original problem for insight.

The computer can run these trials much more quickly than any human can. If you have a Macintosh, you can download a handy program for solving this problem.

Once you have run some experiments and come up with some expected values, try your hand at finding an analytical solution.