Before revision:  Finally, we see that small deviations from the optimal solution can lead to dramatic violations of the constraints  .
After revision:  Finally, we see that small deviations from the optimal solution can lead to dramatic violations of the constraints We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population .