Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.