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 effect of waning on transmission dynamics before vaccination begins. Besides waning, we varied overall transmissibility, the delay from beginning vaccination to reaching specified infection levels, and type specific virus characteristics. We observed an increasing range of vaccination levels that resulted in long periods of silent circulation after eliminating paralytic polio cases 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 seen the threat of silent circulation. They used models with no or very short duration waning and they lacked identifiability of waning effects on silent circulation because they fit models only to paralytic polio case counts. Our analyses show that nearly identical polio case count patterns can be generated by a range of waning patterns that in turn generate diverse silent circulation risks. We conclude that the risks of prolonged silent circulation are real but unquantified, that vaccinating adults with waned immunity will reduce those risks, and that intensive environmental surveillance will be needed to detect this risk before stopping OPV.