Security properties are within the fundamental concerns in the original protocol stack of named data networking (NDN) paradigm. However, NDN still cannot evade some serious network attacks, such as the notorious interest flooding attack (IFA). To mitigate the IFA, interest Negative ACKnowledgments (NACK) may be one of the best countering candidates in NDN, yet does not attract enough concerns. In this paper, we first present a more powerful type of IFA using interest packets with real names rather than spoofed ones to confuse detections. Then, we evaluate the effectiveness of interest NACK on mitigating IFA via a modified susceptible-infected-susceptible epidemic model. In this quantitative analysis tool, we introduce a variable curing parameter to accurately characterize the impact of interest NACK on chosen NDN routers. Moreover, we derive the upper bound for the infection fraction of NDN routers with and without interest NACK, and deduce the relationship between the fraction of total infected nodes and those with NACK implementation. In addition, the accuracy of the proposed model is verified by extensive simulations. To the best of our knowledge, this is the first attempt to theoretically analyze the NDN NACK mechanism on mitigating IFA via the epidemic theory.