A really interesting Calculus word problem: When should the Health Department start an aggressive vaccination program?

The problem:

Suppose the Health Department has been monitoring flu outbreaks continuously over the last 100 years
and has found that the number of infections, I(t), can be modeled by a function, I(t), where t is in months and I is measured in 100; 000s of individuals. The Health Department wantsto begin 5 years of intensive vaccination and quarantine at a time when the flu virus is at a 5-year minimum average. If we assume t = 0 is January 1, 2015, when should they begin the program?

Check out the solution and discussion here!