The Global Polio Eradication Initiative (GPEI) continues to make progress toward eliminating all paralytic cases caused by wild polioviruses (WPVs). The GPEI primarily relies on routine immunization (RI) and supplemental immunization activities (SIAs) using the live, attenuated oral poliovirus vaccine (OPV), [1,2] a comprehensive surveillance system, and aggressive outbreak response [3,4]. Typical estimates suggest that permanent paralytic poliomyelitis may occur at a ratio of approximately 1 case per 200 WPV serotype 1 (WPV1) infections on average in immunologically naïve (i.e., fully susceptible) individuals [2,5], with lower ratios around 1 in 2000 and 1 in 1000 for WPV2 and WPV3, respectively [5-7]. Previously vaccinated or infected individuals can also become asymptomatically infected and potentially participate in poliovirus transmission despite remaining protected from paralytic poliomyelitis, [7-9] which effectively decreases the overall apparent paralysis-to-infection ratio for the entire population. The use of OPV leads to a very small fraction of vaccine recipients (or their close contacts) developing vaccine-associated paralytic polio (VAPP) at historical rates of approximately 1 case per 2.5 million doses distributed in the United States [10] and 2.9-4.7 cases per million births worldwide in OPV-using countries, giving an estimated global burden of about 300-500 cases per year [11]. In addition, as a small mRNA virus, OPV can lose its attenuating mutations and vaccine-related viruses revert back toward WPV to become a circulating vaccine-derived poliovirus (cVDPV), which occurs in the context of prolonged circulation in populations with high susceptibility and can lead to outbreaks [12]. Moreover, in a very small number of individuals with B-cell immunodeficiencies, receiving OPV can lead to prolonged or chronic infections and the development of immune deficient vaccine-derived polioviruses (iVDPVs) [13]. Given these complications, the GPEI expects to coordinate the cessation of OPV use after global eradication of WPVs to minimize the risks associated with live polioviruses (LPVs, i.e., WPVs, VDPVs, OPVs, and OPV-related viruses) [4,14]. At that time, inactivated poliovirus vaccine (IPV) [15] will represent the only vaccine option [16]. However, OPV cessation of any given serotype cannot safely occur until assurance of global interruption of transmission of that serotype. Because the majority of poliovirus infections occur asymptomatically, the possibility of silent circulation complicates the confirmation of local and global interruption of WPV or cVDPV transmission.

A previous statistical analysis [17] and a mathematical infection transmission model of a simple and small hypothetical population [18] that assumed perfect surveillance suggested that it takes approximately 3-4 years without WPV-caused paralytic cases to achieve 95% confidence about the interruption of transmission. A reanalysis of one of these studies [18] demonstrated how varying assumptions that reflect actual conditions about population immunity, vaccination strategies, and seasonal fluctuations in transmissibility impact estimates of the probability and duration of silent circulation [19]. The reanalysis also identified the need to consider the role of previously-vaccinated or infected individuals (i.e., partially infectible individuals) who remain immune to paralytic disease, but not to reinfection, and their potential participation in silent transmission of the virus [19,20]. The reanalysis confirmed the importance of the paralysis-to-infection ratio (PIR) as a key input, [18,19] which suggests the need to perform separate analyses for each serotype. While the reanalysis provided several insights relevant to current conditions, it relied on a hypothetical population, the use of a highly-simplified transmission model that included either OPV or IPV, and it did not account for imperfect surveillance [19]. In this paper, we seek to characterize the confidence about no circulation as a function of time without detected events (i.e., cases or positive sewage samples) in populations with relatively recent circulation. We model populations that may represent conditions like the actual last global reservoirs of WPV transmission and the actual environmental WPV detection that occurred in Israel in 2013. Prior to discussing the model and methods, the next section provides an overview of the different components of polio surveillance, which provides important context about the types, quality, and timing of information available.

We build on our understanding of poliovirus surveillance and prior comprehensive poliovirus infection transmission models [7,20,41-43] to estimate the confidence about (probability of) no circulation in each modeled population as a function of the time since the last detected event. We model populations with relatively recent WPV transmission (both endemic and imported) that rely on AFP surveillance and the actual environmental surveillance detection of WPV serotype 1 (WPV1) that occurred in Israel in 2013 [44]. Although Nigeria started some environmental surveillance efforts in 2011, the scale of these efforts until recently remained relatively small, and consequently we do not consider the potential impact of this environmental surveillance. We recognize that only increasingly localized and shrinking geographic areas in three countries (i.e., Afghanistan, Nigeria, and Pakistan) maintain indigenous WPV1 transmission, but importations into previously WPV-free countries continue to pose a threat of re-established transmission and potential silent circulation, [1] and the emergence of cVDPVs pose a real threat [12]. Consequently, we focus on identifying some scenarios that reasonably represent different types of areas and conditions that warrant modeling because of their population immunity, characteristics, and/or surveillance quality. Similar to prior studies [18,19] this analysis focuses on the detection within a closed population in which an LPV might circulate silently (i.e., without detection).

The model divides the population according to immunity states, including fully susceptible individuals (i.e., those never infected with LPVs or successfully IPV-vaccinated), maternally immune individuals (i.e., children born to mothers with any active recent or historic immunity), and partially infectible individuals (i.e., those who acquired immunity from 1, 2, or 3 or more prior successful IPV doses, or from 1 or 2 or more prior LPV infections) [7]. As noted in the prior section, partially infectible individuals benefit from complete, permanent protection from paralysis; however, re-infection can occur and lead to different degrees of participation in poliovirus transmission (depending on their immunity state and extent of mucosal immunity waning). Only fully susceptible and maternally immune individuals with insufficient maternal antibodies remaining to provide protection can become paralyzed when infected with a LPV for the first time. The model includes a 6-stage infection process, a 5-stage immunity waning process, and a 20-stage poliovirus reversion process for both fecal-oral and oropharyngeal routes of transmission. We divide the population into a number of age groups that varies depending on the modeled situation. However, regardless of the scenario settings we combine the age groups into 3 preferentially mixing age groups (i.e. 0-4, 5-14, and 15 or more years) [7,20,41-43]. We characterize population immunity to poliovirus transmission by computing the age-and-sub-population-mixing-adjusted effective immune proportion (EIPM) [42]. We also define an immunity threshold, EIP*, which depends on the basic reproductive number for the population and virus serotype (R₀), with EIP* = (1- 1/R₀). For EIPM > EIP* infections eventually die out [42]. We use the EIPM and R₀ to estimate the net reproductive number (Rn), defined as (1-EIPM) × R₀, which represents the average number of secondary transmissions generated by a single infection given the population immunity at the time Rn has a threshold of 1 regardless of the assumed R₀ for a population and serotype. Thus, for Rn > 1 (i.e., EIPM < EIP*) continued transmission can occur, while for Rn < 1 transmission will die out (i.e., EIPM > EIP*). We model 4 populations (i.e., qualitatively different conditions related to the transmission potential, expected population immunity at the time of WPV1 or WPV3 certification, OPV take rates, and surveillance quality) as shown in Table 1 [41-44]. For each population, we specify demographic information, poliovirus transmissibility and seasonality, and the history of live poliovirus exposure, including OPV use for RI or SIAs. The Additional file 1 provides details about the model, including updates for recent immunization activities and assumptions used to model die-out and characterize population immunity. We run the existing deterministic poliovirus transmission model for each situation and serotype up to a point in time shortly before die-out occurs (Table 1) and then transform it to a discrete, stochastic model that we run 1,000 times (see Additional file 1). For the situation representing Israel, we focus on iterations consistent with the outbreak response that actually occurred (i.e., we only allow the iterations with one or fewer paralytic cases occurring after mid-July 2013, because the occurrence of actual cases prior to that date would have likely changed the outbreak response).Table 1

List of scenario-specific model inputs

We synthesize the following results, similar to prior analyses [18,19]:

POE - the probability of eradication defined as the fraction of stochastic iterations in which die-out occurs (i.e., prevalence below the transmission threshold)

For this analysis, we focus on detected-events (i.e., detecting cases from AFP surveillance and positive isolates that indicated the presence of infections from environmental surveillance) and the DEFP instead of the case-free period used previously [18,19] to account for the different information provided by the two components of poliovirus surveillance used. To emphasize our focus on no circulation in the absence of cases and in the context of less than perfect surveillance, we use the time of undetected circulation (TUC) rather than the time of silent circulation (TSC) assuming perfect surveillance used previously (i.e., TUC with perfect surveillance equals TSC) [18,19].

We explicitly consider the impact of imperfect information from surveillance and provide a comparison to perfect information as a point of reference. For each modeled situation, we define a detection function (DF) as an indicator of overall surveillance quality and to account for imperfect surveillance. The detection function describes the probability of detecting the i^th case (p_i, used for AFP surveillance) or i^th sewage sample that contains poliovirus (s_i, used for environmental surveillance) in a cluster. We define a cluster as a series of sequential detected cases or sequential virus detections in sewage in a given geographical subpopulation, with no more than one year between successive detections. For environmental surveillance, detection depends on the number of individuals excreting poliovirus into the sewage system in a geographical subpopulation. We define the effective infectiousness-weighted number of infectious individuals (EI) and compare this to the threshold (EI*) required for the system to detect the virus in the sewage. We define s_i as the probability of detecting poliovirus in the i^th sewage sample given that EI > EI*. Thus, each time when sample collection should occur (i.e., every month) we check whether the weighted number of excreting individuals exceeds the EI*.

We characterize the different inputs for surveillance quality assuming variable levels of quality of the (sub)national surveillance systems, with better systems receiving relatively higher values for all p_i. This framing allows for a relatively higher probability of missing the first case, with decreasing probabilities of missing subsequent cases in the same temporal cluster for the fixed spatial area, depending on the situation-specific assumptions (Table 1, details on methods and assumptions provided in the Additional file 1).

Figure 2 presents the confidence about no circulation as a function of time without detected events, with black horizontal lines at the top showing the 99% (small dots) and 95% (larger dots) levels for reference. Each solid line (red, green, blue) represents the result using perfect AFP surveillance for the indicated serotype. Each dotted line of the corresponding color presents the impact of imperfect AFP surveillance (Figure 2a-d) or environmental surveillance (Figure 2e), as characterized for the different detection functions in Table 1.Figure 2

Confidence about no circulation as a function of the detected-event free period and lines provided to indicate 95% and 99% for reference. a). Northern India. b). Northwest Nigeria 2014 current path (note change of x-axis scale). c). Northwest Nigeria increased tOPV (note change of x-axis scale). d). Tajikistan. e). Israel.

Current policies require a period of at least 3 years of no paralytic polio cases detected by the AFP surveillance system to certify an area as free of WPV. Our analysis suggests that specific situations and serotypes will differ such that 3 years may imply more or less than 95% confidence and demonstrating that the quality of the information impacts the time. Policy makers should recognize that choices made to achieve and maintain high levels of population immunity could impact the success or failure of polio eradication and the investment required in ongoing surveillance to ensure confidence about the absence of silent circulation when observed cases and/or signals from environmental surveillance stop [46,47]. Correlation between the populations at greatest risk of undetected circulation and poor surveillance quality suggest the need to specifically focus on underserved areas. Recognizing these areas may motivate the exploration of the development of environmental surveillance systems that could potentially reduce the time required to reach a high level of confidence about the absence of circulation in these areas, which will likely drive global decision making. Considerable variation in poliovirus surveillance activities (and the associated population-specific values for the components in Figures 1b-1d) leads to different degrees of quality, and policy makers will need to consider the impacts of imperfect information.

Early detection of circulating infections provides an important opportunity to increase population immunity, decrease Rn, and prevent any cases from occurring. In Israel, population immunity fell below the threshold and transmission occurred, but this did not lead to cases due to the protection from paralysis provided by high coverage with IPV. The ability of high coverage with IPV to prevent cases but potentially not prevent or disrupt transmission in some situations may decrease the ability to detect transmission using AFP surveillance.

Serotype differences in the PIRs imply significant differences between the relevant DEFP values, which may influence OPV cessation policy development. For example, the relatively low PIR of cVDPV2, if combined with insufficient population immunity against serotype 2 and heterogeneity in surveillance quality in regions like northwest Nigeria, may lead to significant increases in the DEFP values, which would indicate the need for longer periods of time required without detected events to certify the interruption of LPV transmission. Some countries will need to increase population immunity prior to OPV cessation to safely stop LPV transmission and rapidly obtain confidence about the absence of transmission.

Our analysis remains limited by the model assumptions, including assumptions made to translate the differential-equation based model into a stochastic model related to use of the transmission threshold. For example, using the criterion for die-out in this analysis represents prevalence below the transmission threshold rather than absolute 0 total infected individuals. Nonetheless, we believe the analysis provides useful insights relevant to the polio endgame.

As we consider the prerequisites for OPV cessation and approach key decision points, countries will need to recognize that increasing population immunity and the actual quality of surveillance will impact the risks of undetected circulation and the confidence associated with different time periods of no observed cases. The potential degradation of surveillance quality suggests the need to ensure a commitment to high-quality surveillance and/or requires a longer time of no detected events. Environmental surveillance may provide an important opportunity to reduce the time required to feel confident about the absence of undetected circulation, although the value of the information provided will depend on the system design.