Although much research effort has been directed toward refining algorithms for disease outbreak alerting, considerably less attention has been given to the response to alerts generated from statistical detection algorithms. Given the inherent inaccuracy in alerting, it is imperative to develop methods that help public health personnel identify optimal policies in response to alerts. This study evaluates the application of dynamic decision making models to the problem of responding to outbreak detection methods, using anthrax surveillance as an example. Adaptive optimization through approximate dynamic programming is used to generate a policy for decision making following outbreak detection. We investigate the degree to which the model can tolerate noise theoretically, in order to keep near optimal behavior. We also evaluate the policy from our model empirically and compare it with current approaches in routine public health practice for investigating alerts. Timeliness of outbreak confirmation and total costs associated with the decisions made are used as performance measures. Using our approach, on average, 80 per cent of outbreaks were confirmed prior to the fifth day of post-attack with considerably less cost compared to response strategies currently in use. Experimental results are also provided to illustrate the robustness of the adaptive optimization approach and to show the realization of the derived error bounds in practice. Copyright © 2011 John Wiley & Sons, Ltd.