Silent circulation of polioviruses without poliomyelitis cases could threaten eradication when oral polio vaccine (OPV) use is stopped worldwide. Waning immunity promotes silent circulation by increasing poliovirus transmission from individuals not at risk of paralytic polio. There is limited data on temporal patterns of waning. Accordingly, we modeled a range of waning patterns, scaled from fast but shallow to slow but deep, while keeping constant the overall effect of waning on transmission dynamics before vaccination begins. Besides waning, we varied overall transmissibility, the delay from beginning vaccination to reaching specified vaccination levels and type specific virus characteristics. We observed that the width of the range of vaccination levels that resulted in long periods of silent circulation after eliminating paralytic polio cases increased as the delay in reaching final vaccination levels increased. The extent of silent circulation was higher when waning was slower and deeper, when transmissibility was higher, and when virus was type 3. In our model, modest levels of vaccination of adults reduce silent circulation risks. These modeled patterns are consistent with very long silent circulation mainly emerging as a threat to OPV cessation in the last places from which polio cases are eliminated. Our analyses indicate why previous modeling studies have not found the threat of silent circulation that we find. They either used fast and shallow waning patterns that seem unlikely, and/or they depended on fitting models to paralytic polio case counts. Our analyses found that nearly identical polio case count patterns over time are consistent with a range of waning patterns that generate diverse silent circulation risks. We conclude that studies assessing immunity waning dynamics are needed before OPV is stopped. We also conclude that vaccinating adults before stopping OPV will help insure against persisting silent circulation when OPV use is stopped.