A modern flu is spread throughout a small community with a fixed population of size n. The disease is spread through contact between infected persons and persons who are susceptible to the disease. Assume that everyone is susceptible to the disease initially and that the community is contained so that no one leaves the community.
The model given in (12.39) can be used to model the epidemic throughout the community. Suppose b = 0.002; a = 0.7, and n = 1000.

a. Solve the system for the following initial conditions: I (0) = 2,5,10, and 100.

b. Using, I (0) = 2, 5,10, and 100 and S (0) = n–I (0), resolve the system and interpret the result.