Flu Epidemic

A certain population has 20,000 people. The population is hit by a strain of flu. 1% of the susceptible population per day is stricken. The flu effects last 5 days, after which the effected person is then immune to this virus. 10% of the population is naturally immune to the virus.

  1. If the epidemic were allowed to run its course, how long would it take for the entire population to be immune?

  2. The Health Service would like to institute an immunization program in an attempt to knock out the epidemic quickly, within a month, if possible. However, they would also like to inoculate as few people as possible because the serum does occasionally make people feel sick.

    Create a plan that would keep the flu from reaching epidemic levels, but would also minimize inoculating people unnecessarily.