Most recent surveys and reviews on Influential Node Ranking Methods (INRMs) hightlight discussions on the methods' technical details, but there still lacks in-depth research on the fundamental issue of how to verify the considerable influence of these nodes in a network. Compared to conventional verification models such as cascade failure and linear threshold, the epidemic model is more widely used. Accordingly, we conducted a survey of INRM based on epidemic model on 81 primary studies and analyzed their Capability and Correctness which we defined in our work. Our study categorized 4 types of networks used by INRM, classified 7 categories of INRMs for analyzing the networks and defined 2 evaluation metrics set of Capability and Correctness for evaluating INRM from Ranking Rationality Perspective. We also discussed particular real-world networks that were used to evaluate INRM and the Capability and Correctness of different INRMs on ranking nodes in specific networks. This is, as far as we know, the first survey aimed at systematically summarizing the Capability and Correctness of INRM. Our findings can assist practitioners and researchers in choosing and comparing INRMs and identifying research gaps.