If the world can successfully control all outbreaks of circulating vaccine-derived poliovirus that may occur soon after global oral poliovirus vaccine (OPV) cessation, then immunodeficiency-associated vaccine-derived polioviruses (iVDPVs) from rare and mostly asymptomatic long-term excretors (defined as ⩾6 months of excretion) will become the main source of potential poliovirus outbreaks for as long as iVDPV excretion continues. Using existing models of global iVDPV prevalence and global long-term poliovirus risk management, we explore the implications of uncertainties related to iVDPV risks, including the ability to identify asymptomatic iVDPV excretors to treat with polio antiviral drugs (PAVDs) and the transmissibility of iVDPVs. The expected benefits of expanded screening to identify and treat long-term iVDPV excretors with PAVDs range from US$0.7 to 1.5 billion with the identification of 25–90% of asymptomatic long-term iVDPV excretors, respectively. However, these estimates depend strongly on assumptions about the transmissibility of iVDPVs and model inputs affecting the global iVDPV prevalence. For example, the expected benefits may decrease to as low as US$260 million with the identification of 90% of asymptomatic iVDPV excretors if iVDPVs behave and transmit like partially reverted viruses instead of fully reverted viruses. Comprehensive screening for iVDPVs will reduce uncertainties and maximize the expected benefits of PAVD use.