In this talk, we investigate a large SIR system (Susceptible, Infected, Recovered) where agents can vaccinate. We show that this system admits a unique stable vaccination schedule for each agent: vaccinate at full rate until some point in time when vaccination is no longer desirable. We also prove that the vaccination strategy minimizing the total cost for the population is a similar scheduling policy, but with a different stopping time. To encourage individual optimal vaccination behaviors that lead to the common good, vaccination should be subsidized to compensate for the gap between the two stopping times.