Bio-terror events are accompanied by severe uncertainty: great disparity between the best available data and models, and the actual course of events. We model this uncertainty with non-probabilistic information-gap models of uncertainty. We focus on info-gaps in epidemiological models, in particular, info-gaps in the rate of infection. We define the robustness to uncertainty as a function of the required critical morbidity resulting from the attack. We show how preferences among available interventions are deduced from the robustness function. We demonstrate the irrevocable trade-off between robustness and demanded performance, and we show that best-estimated performance has zero robustness. We present a theorem concerning the reversal of preferences between available interventions, and illustrate it with a numerical example. We also consider the opportuneness inherent in the uncertainty and how preferences are formulated by attempting to enhance the possibility of favorable windfall.