Polio is a fecal-oral disease that can cause fever and flu-like symp- toms, and, in more rare instances, acute flaccid paralysis (AFP). One characteristic of poliovirus is asymptomatic transmission amongst in- dividuals who have already had a poliovirus infection. This allows the virus to silently circulate in an endemic population unless a surveil- lance system is put into place. Eradication efforts have reduced the regions of endemic circulation down to three localities. However, due to infrequent first infections and poor surveillance, it can be difficult to determine when the virus has been eliminated from the population. The silent circulation statistic is used to determine the probabil- ity of polio circulation given an interval of t years without a detected paralytic case. In this talk, we introduce an analytic method of calcu- lating the statistic, examine its nuances, and its sensitivity to model assumptions, using a discrete-individual stochastic counting process model of polio in which immunity is temporary and in which vacci- nation is not included. We show that the assumptions of the statistic present some biases in estimating the probability of silent circulation of polio when applied to small populations, that are not present when applied to large populations under the specified model assumptions. The goal of this analysis is to allow for more robust inferences re- garding the state of polio circulation in a region given paralytic case data.