Management policies for influenza outbreaks balance the expected morbidity and mortality costs versus the cost of intervention policies. We present a methodology for dynamic determination of optimal policies in a stochastic compartmental model with parameter uncertainty. Our formulation is based on Bayesian conjugate updating in conjunction with stochastic control methods for optimal stopping. Facing a high-dimensional control problem, we construct a new Monte-Carlo computational approach that searches the full set of sequential control strategies. As a running example, we study a stochastic SIR-model with isolation and vaccination as two possible interventions. We also investigate the value of information and effect of various cost structures. Numerical simulations demonstrate the realized cost savings of choosing interventions based on the computed dynamic policy over simpler decision rules.