The probability that an individual with degree k will spark an epidemic is equal to the probability that transmission along at least one of the k edges emanating from that vertex will lead to an epidemic. For any of its k edges, the probability that the disease does not get transmitted along the edge is 1 − T. The probability that disease is transmitted to the attached vertex but does not proceed into a full-blown epidemic is Tu, where u is the probability that a secondary infection does not spark an epidemic. Thus, the probability that an individual will spark an epidemic is 1 − (1 − T + Tu) k .