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Estimation of polio infection prevalence from environmental surveillance data

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Science Translational Medicine  29 Mar 2017:
Vol. 9, Issue 383, eaaf6786
DOI: 10.1126/scitranslmed.aaf6786

Keeping an eye on polio

As the eyes are a mirror of the soul, a city’s sewage is a reflection of its people’s health. Berchenko et al. take advantage of a natural experiment in southern Israel to quantify this relationship for polio. By measuring virus shed into sewage waste in cities in which a known number of people received a live polio vaccine, the authors created tools that can be used to monitor polio incidence in other cities. Thus, virus levels in sewage waste can give an early warning of the reappearance of viral disease or verify its absence.

Abstract

A major obstacle to eradicating polio is that poliovirus from endemic countries can be reintroduced to polio-free countries. Environmental surveillance (ES) can detect poliovirus from sewage or wastewaters samples, even in the absence of patients with paralysis. ES is underused, in part because its sensitivity is unknown. We used two unique data sets collected during a natural experiment provided by the 2013 polio outbreak in Israel: ES data from different locations and records of supplemental immunization with the live vaccine. Data from the intersecting population between the two data sets (covering more than 63,000 people) yielded a dose-dependent relationship between the number of poliovirus shedders and the amount of poliovirus in sewage. Using a mixed-effects linear regression analysis of these data, we developed several quantitative tools, such as (i) ascertainment of the number of infected individuals from ES data for application during future epidemics elsewhere, (ii) evaluation of the sensitivity of ES, and (iii) determination of the confidence level of the termination of poliovirus circulation after an outbreak. These results will be valuable in monitoring future outbreaks with ES, and this approach could be used to certify poliovirus elimination or to validate the need for more containment efforts.

INTRODUCTION

The Global Polio Eradication Initiative has reduced the burden of poliomyelitis by >99% since its launch in 1988, leaving only three endemic countries, and is one of the most important public health initiatives of current times (14). Nevertheless, final steps toward polio eradication have encountered unexpected difficulties. One obstacle is the reintroduction of wild poliovirus (WPV) from an endemic country into previously polio-free countries; in particular, during 2013, the eradication program suffered a severe setback from the reintroduction of WPV to several countries that had been polio-free [Egypt, Israel, and Syria, as well as the Horn of Africa (3)]. This led the director general of the World Health Organization (WHO) to pronounce the international spread of WPV a Public Health Emergency of International Concern (7).

Israel had been considered poliomyelitis-free since the 1988 outbreak, which resulted in 15 paralytic cases (22). In 2005, Israel changed from a sequential schedule of inactivated polio vaccine followed by oral polio vaccine to exclusive use of inactivated polio vaccine. The oral vaccine induces a strong gut immunity that limits virus transmission, whereas the inactivated vaccine confers humoral immunity that protects an individual from paralysis but has limited effect on transmission (9). The oral vaccine poses a minor risk of vaccine-associated paralytic polio for nonimmune recipients and their unimmunized contacts (23); nevertheless, because it was free of poliomyelitis, Israel decided to discontinue the use of the oral vaccine in their vaccination programs.

The Israeli Ministry of Health has been monitoring sewage for polio since 1989, with composite sewage samples collected monthly at the mouth of sewage treatment facilities (24) from sentinel sites covering 30 to 40% of the Israeli population (25). During the spring of 2013, WPV was detected by routine environmental surveillance (ES), revealing asymptomatic transmission without clinical cases (a silent epidemic) (26). The first detection of WPV, on May 29 in Rahat, a Bedouin town in the southern part of Israel, was of a type 1 poliovirus related to strains found in Egypt at the end of 2012 (25). Additional positive samples were later identified, mainly in the south of Israel but also in other locations in the central and northern parts (25). Transmission during the outbreak was concentrated in children under the age of 10, reflecting their vaccination history with inactivated polio vaccine only (27).

As a result of the alarming presence of WPV, the authorities intensified ES (fig. S1) and launched a national supplementary immunization program with the oral polio vaccine, covering about 80% of the total population and more than 90% of the Bedouin population, in whom most of the transmission was seen (12).

To contain a polio reintroduction, the virus must be quickly detected, and an intense vaccination campaign should be launched immediately. Therefore, the Global Polio Eradication Initiative included surveillance as a key priority in its new strategic plan for polio eradication (8). There are two surveillance alternatives. The first traditional approach, acute flaccid paralysis surveillance, is based on reports of clinical paralytic cases. The second approach, ES, is based on the detection of poliovirus excreted by infected individuals (both symptomatic but mainly asymptomatic) into sewage or wastewaters. ES is especially useful in communities with high inactivated polio vaccine coverage, which confers good protection against paralysis but has limited effect against transmission (9, 10). In such communities, ES could shorten the time of detecting polio reintroduction, compared to acute flaccid paralysis surveillance, which could detect new outbreaks at a very late stage, only after a paralytic case (10, 16). Today, inactivated polio vaccine is used in most developed countries, and in many of them, the vaccine coverage is high. Under such circumstances, the reintroduction of WPV can lead to asymptomatic polio circulation (silent transmission), such as occurred in Israel (11, 12).

Although the Global Polio Eradication Initiative’s new Strategic Plan includes increased use of ES in polio surveillance (8), currently, ES can only be used semiquantitatively (presence or absence of the virus in the sample without an estimate of the number of shedders and/or sensitivity). Information regarding ES sensitivity is lacking; to date, quantitative observations and experimental results are limited (1315).

Because of the difficulties in obtaining ES data, investigators have resorted to mathematical modeling and simulations to evaluate the effect on detection sensitivity of parameters such as the volume and number of samples collected (15). Mathematical modeling and simulations were also used recently for describing and studying the 2013 Israeli outbreak (16).

Spiking trials, in which a known amount of virus is actively poured into the sewage by the researchers (to be recovered downstream) (17, 18), do not link the virus detected to the organic shedding of a live virus. Studies in which the live virus is monitored, for example, after a national vaccination day with the oral polio vaccine, do not determine the number of shedding individuals contributing to the sewage (14, 1921). Often, ES data are presented only as a semiquantitative present/absent dichotomy.

To improve the successful use of ES for surveillance, we have used the data collected during the 2013 silent polio outbreak in Israel to estimate the number of infected individuals in a community from ES measurements, to evaluate the sensitivity of ES, and to indicate when eradication has been achieved using ES measurements. We then confirm the generality and robustness of the approach.

RESULTS

To develop quantitative use of ES, we analyzed the number of oral polio vaccine–derived viral particles found with a plaque assay (25) in the sewage in relation to the number of children vaccinated during the Israeli supplementary immunization campaign. We used data from seven selected towns with at least four positive measurements between August 5 and September 30, a well-defined residential area, and no overlap or spillage from neighboring sewage sources (Table 1 and Materials and Methods).

Table 1. The seven cities and towns studied here.
View this table:

We first correlated a time series of the number of viral particles detected in the sewage with the number of children vaccinated for each of the seven towns. As an example, data from Beer-Sheva (the largest city in southern Israel) are shown (Fig. 1). These comparisons indicated that vaccination was followed by appearance of viral particles in the sewage about 7 to 14 days later (R2 = 0.79), corresponding with previous findings (13). Correlations for 0 to 7 and 14 to 21 days later were much lower (R2 = 0.24 and 0.12, respectively). We then fit a linear regression of the logarithm (log10) of the number of viral particles detected in the sewage of a particular town at a specific time of inspection on the logarithm of the number of people vaccinated in that town 7 to 14 days before the sewage measurement, normalized to the volume of sewage produced by the town’s population (Fig. 2 and Table 3). Three models were examined: (i) where the intercept and the slope of the regression line were the same for each town, (ii) where the slope was the same but the intercept varied across towns, and (iii) where both the slope and the intercept varied across towns. Model (ii) provided the best fit to the data [AIC, 39.8; compared to 49.6 and 43.2 for models (i) and (iii), respectively; see Table 2]; the common slope was estimated to be 0.95 [95% confidence interval (CI), 0.82 to 1.10], the intercepts that varied across towns had a mean of 6.06 with an SD of 0.22, and the residual error had an SD of 0.31. The model predicts that the logarithm of the number of viral particles in the sewage per vaccinated person was 6.06 ± 0.38 SD per day (mean ± SD) during the 7- to 14-day period (Table 3).

Fig. 1. The number of children vaccinated daily in Beer-Sheva (the biggest city in the south of Israel) (blue) and the number of virus particles detected (per sample) in its sewage (red).

These data and pairs of time series data for other cities and towns in Israel are shown in fig. S1.

Fig. 2. Relationship between viral particles detected (normalized to the entire volume of the city’s sewage) and number of people vaccinated.

The number of virus particles detected during sewage measurement as a function of the number of people vaccinated 7 to 14 days before sewage measurement (normalized by the city or town sewage daily volume production; see the Supplementary Materials). Linear regression of all 47 data points from all seven cities and towns, on a log10 scale, yields R2 = 0.79.

Table 2. Akaike information criterion and Bayesian information criterion scores for the various model examined.

AIC, Akaike information criterion; BIC, Bayesian information criterion.

View this table:
Table 3. Estimated model parameters.

Embedded Image depicts the estimated SD of ε, SD(ε); note that thus its CI depicts the variance of the estimator of the variance. The same applies, mutatis mutandis, to Embedded Image and Embedded Image. Summation of the variance components of the top random intercept model provides a marginal SD of 0.38.

View this table:

Under routine ES, the observed variable is the number of particles within a sample (including the possibility of zero particles), and our aim has been to estimate the number of shedding individuals. Thus, the roles of the independent variable (previously, the number of people) and the dependent variable (previously, and mechanistically, the number of particles detected) are now exchanged. In other words, the (random intercept) regression is now:Embedded Image(1)where Embedded Image and the variances of Embedded Image and Embedded Image (both having mean zero) are obtained by regressing the number of people vaccinated on the number of particles detected (Table 3, bottom).

To assess the ability to estimate the number of shedders from future ES measurements in different locations, we conducted a cross-validation analysis using a leave-one-out technique. Figure S3 shows the predicted numbers of shedders, with their 95% CIs, plotted against the true numbers, demonstrating that almost all predictions fall close to the true numbers, corroborating that Eq. 1 can predict the number of shedders in new locations.

It was also possible to further validate externally the ability of Eq. 1 to estimate the outbreak size because of the availability of stool samples from the outbreak (27). In Rahat, the epicenter of the outbreak, a sewage sample immediately before the supplementary immunization campaign (5 August 2013) found 175 particles. Applying Eq. 1 then provided an estimate of 1663 shedders (95% CI, 360 to 7710).

We compared this estimate to an estimate based on the stool samples taken in Rahat 2 weeks before the ES sample was taken (27). Of the 546 stool samples taken from children under the age of 10, 26 (4.8%) were positive for WPV (27), leading to an estimate of 700 children shedding WPV of all of the 14,500 children under 10 years of age in Rahat. Alternatively, if we assume that the prevalence in adults equals the prevalence in children [although the survey in (27) focused on children because of the epidemiological understanding that transmission is more likely concentrated in children (12)], then an estimate of 2800 shedders in Rahat is obtained (of the 59,000 total population; see Table 1). The estimates from both scenarios fall well within the CI of the ES-based estimate.

Our methodology also allows an assessment of the limit of detection of the ES approach. The x-axis intercept in fig. S2 (10−2.61/400) provides a rudimentary threshold for the detection of one secreting person per 400 m3/day of sewage production [see the discussion in (13) for a crude calculation of feasibility of the detection of ES].

Similarly, and in a more formal manner, quantitative ES can also be used to verify the end of polio circulation. The probability of observing zero poliovirus particles, when there is one shedding individual, can be modeled with the Poisson distribution [as done in (15)]. By using the above findings (Table 3 and eq. S1), we obtained a P value for rejecting the hypothesis that “poliovirus is circulating within the population” (see the Supplementary Materials for further details).

The last positive sample from Rahat ES was detected in January 2014; on the basis of the subsequent negative sample (that is, no virus particles detected) obtained at the end of January 2014, the calculated P value for rejecting the hypothesis of undetected polio circulation in Rahat was 0.85 (see the Supplementary Materials). However, since then, all 53 subsequent samples taken during 2014 were also negative. Assuming that each measurement is independently distributed, these additional samples strengthen the certainty in a multiplicative manner, decreasing the P value to 0.8553 = 0.00018.

The importance of the model for the purpose of polio eradication deserves emphasizing: Currently, a measurement of zero particles (that is, no detection) cannot be scientifically or statistically interpreted. Our model provides an objective and quantifiable method for rejecting the hypothesis that poliovirus is circulating within the population and can aid in calculating the sampling frequency needed for determining whether eradication has been reliably established.

DISCUSSION

If there had been only acute flaccid paralysis surveillance during the silent polio epidemic in Israel, the outbreak would likely have been detected much later and only after the occurrence of a case of paralysis. Nevertheless, despite advanced ES in Israel, its utilization during the outbreak was only semiquantitative because of the lack of a good quantitative understanding of the method. Supplementary immunization was initiated more than 2 months after the first detection of WPV by ES. The delay in the vaccination campaign was partially a result of lack of a real-time estimation of the extent of the outbreak (12). Only after the results from the stool sampling, indicating that the prevalence of infected children in Rahat was more than 4% at that time, was the magnitude of the epidemic apparent and the need to use the oral vaccine to curtail the outbreak fully understood (11, 12). If the quantitative assessment of ES data had been available, the estimate of 1663 asymptomatic wild-type polio shedders (95% CI, 360 to 7710) in Rahat may have prompted swifter action.

Despite our focus on the Israeli example, it should be emphasized that the methodology described here is readily applicable to other locations worldwide; the only two important factors are (i) adherence to the laboratory protocol described here and (ii) having knowledge of the volume of the sewage reservoir (or having a good estimate of the volume of sewage produced by the city or town; see the Rahat examples in Materials and Methods (“Estimating the infection prevalence” section) and in the Supplementary Materials (“Detection threshold” section).

Quantitative ES can be transformative for polio surveillance and eradication efforts. This methodology allows estimation of a probability P value for testing the hypothesis that virus transmission has been terminated, both locally and globally. For example, we found in Rahat an 85% chance of obtaining a false negative in a single sample, given that one member of the population is infected. Given a required significance level for a test of no eradication, it is straightforward to calculate the necessary sampling frequency to achieve the desired P value if the outbreak has really terminated (see eq. S1).

With quantitative knowledge of the sensitivity of ES, it would have been possible to estimate the termination of the outbreak in real time. Unfortunately, gaps in quantitative understanding of ES contributed to the decision by the International Health Regulations to include Israel as a state “infected with wild poliovirus but not currently exporting” as late as May 2014 (7). The International Health Regulations criterion for removal from this list is “At least six months have passed without detection of wild poliovirus transmission in the country” (28). The WHO current policy does not distinguish between detection of transmission by acute flaccid paralysis surveillance and detection by ES, yet the sensitivity of the two methods are very different (11). For example, at vaccine coverage rates higher than 90% (in most countries that administer inactivated polio vaccine, the coverage is very high), we find that ES is 103 to 104 more sensitive than acute flaccid paralysis surveillance, given a monthly sampling frequency (see the Supplementary Materials). This suggests that the criteria for evidence of cessation of transmission, which are currently based on the detection of acute flaccid paralysis surveillance cases, are unduly strict when based on good-quality ES data and should be reconsidered on the basis of the quantification described above. The fact that WPV was detected relatively early (3 to 4 months) after the reintroduction of the virus into Israel (29) is an additional indication of the high sensitivity of ES.

ES is now an essential component of the Global Polio Eradication Initiative’s strategy, which in 2016 will enter a new phase with the planned withdrawal of oral polio vaccine for type 2. After withdrawal of oral polio vaccine for type 2, silent transmission could occur in a developing country as a result of the loss of mucosal immunity to WPV type 2 (30). Establishing ES in countries with a high risk of reintroduction will allow earlier detection, resulting in more rapid initiation of supplementary immunization activity. Moreover, quantitative ES can be used during immunization to determine the appropriate sampling frequency required to provide the required confidence for deciding when polio vaccination (both inactivated and oral vaccines) can be discontinued.

There are several limitations to our approach. The quantification and parameter estimates obtained here are based on particles of the oral polio vaccine strains and not WPV. The oral strains might differ from WPV in two main aspects: (i) the mean duration of viral shedding and (ii) the amount of viral shedding. In addition, the vaccination background (that is, if an individual was previously vaccinated with inactivated or oral vaccine) has effects on both the duration and the amount of viral shedding (9). Similarly, bivalent oral polio vaccine containing serotypes 1 and 3 was administered during the immunization campaign but in focusing on “any poliovirus vaccine strain” isolation, sensitivity might be overestimated. However, it is possible to conduct studies to further examine the differences, and this can be addressed and corrected in a relatively straightforward manner; furthermore, the surveillance and detection of vaccine-derived polioviruses are also of great importance, as the recent outbreak in Ukraine demonstrates (31).

Although the point estimates that we use may not be accurate, they can be used as bounds with great assurance—a lower bound for the number of shedders and an upper bound for the P value [because presumably WPV shedding is greater than the amount of shedding of the oral vaccine (9)]. Having such bounds is also very useful; that is, if the validity of the exactness of statements like “the P value is P = 0.08” might be doubted, an “upper-bound” version (“the P value is P < 0.08”) is both valid and useful.

Care should be taken when interpreting or using these results because they are protocol-dependent and depend particularly on the volume of the sample taken for analysis, as well as on the volume of the entire sewage reservoir in which the virus particles are presumably mixed homogeneously. However, this information is often available or can be obtained readily.

An additional concern is whether cities and towns in Israel reflect other locations worldwide. As discussed above, the situation in Israel is not unique. In addition, we examined diverse sewages (urban, rural, and industrial), and the cross-validation analysis suggests that the findings are robust to such variations once a “sewage production correction” is performed (adding a production-dependent intercept). One possible remaining issue is whether degradation of the virus occurs in Israel at a different rate than other places (for example, temperature dependence). However, the various sewages (urban, rural, and industrial) and conditions (desert to Mediterranean climate) that we examined exhibited similar rates of degradation, suggesting that this should not be a major concern. Moreover, this degradation rate could be easily corrected for in a sample from a new location or by laboratory testing.

MATERIALS AND METHODS

Study design

Our aim was to develop a quantitative approach to use ES and empirically link the number of poliovirus particles found in the sewage to the number of infected people in the population. Because of ethical restrictions, it is impossible to directly conduct a dose-dependent experiment. To overcome such limitations, we combined two different data sets collected during the outbreak in Israel: ES data from different sewages across the country and records of supplemental vaccination from the same locations.

Data collection

Vaccination campaign.

On 5 August 2013, a supplementary immunization campaign was launched in the southern district of Israel to vaccinate all children 0 to 9 years of age who had not received the oral polio vaccine in the past. The vaccine of choice was a bivalent (types 1 and 3) oral polio vaccine. Two weeks later, following continuous transmission of the poliovirus, the supplementary immunization campaign was extended to the rest of the country (32). The compliance with the vaccination campaign was relatively high with about 80% of the population nationwide and more than 90% of the Bedouin population receiving at least one dose of the vaccine. In towns with persistent findings of wild-type poliovirus in the sewage, a second round of vaccinations was initiated on 7 October 2013 with a coverage of about 53% of the targeted population (26). The Ministry of Health has provided us the data regarding the entire supplementary immunization campaign (that is, numbers of people vaccinated according to date and location; see fig. S1), depicting daily immunization incidence from seven cities and towns in Israel.

Sewage surveillance.

The Israeli Ministry of Health has been monitoring sewage from sentinel sites covering 30 to 40% of the Israeli population [further details in (25)]. Sewage samples (10 liters) were collected over 24 hours at the entrance to sewage treatment facilities using in-line automatic composite samplers or at upstream branch points within the catchment areas of the sewage treatment facilities using automatic Sigma composite samplers (Sigma SD900 automatic samplers, Hach). The composite sample comprised a mixture of 24 or 48 individual samples gathered at timed intervals over a 24-hour period. A volume of 0.5 liters of sampled sewage was concentrated to a final volume of 15 to 20 ml using polyethylene precipitation methods as described (33). The number of virus particles was determined according to the tissue culture plaque assay, in accordance with the recommended protocol by the WHO (34) .

During the silent outbreak, sampling was extended to include highly intensified ES, first in additional communities in southern Israel and subsequently nationwide (see fig. S1 for examples of surveillance data from seven cities in Israel). The number of ES samples collected during the outbreak rose from 12 samples taken during May 2013 to 145 samples taken in August and 53 samples in September, with weekly numbers of 12 to 36 samples (25). Together, between early January and the end of August 2013, 262 sewage samples were tested, mostly between mid-July and mid-August. These comprised 192 samples obtained from 75 sites across Israel, as well as 70 samples obtained from the Palestinian Ministry of Health (25). Sampling frequency over the summer-autumn period was between every 1 or 2 weeks for sites belonging to high-risk locations (25).

Sewage production per city

The detection of the virus in the sewage depends on the virus concentration in sewage, which is a function of the sewage volume (daily production). In a well-mixed, “homogeneous” sewage system, the same number of virus particles (per milliliter) in a small volume of sewage will give a concentration that is proportionally larger than in a larger volume of sewage; therefore, to compare cities and towns with different sewage volumes, it is important to adjust for their daily sewage volume production. Information on sewage volume was provided by the Israel Nature and Parks Authority and the Governmental Authority for Water and Sewerage (see Table 1).

Stool samples

After the detection of WPV, stool surveys were also conducted in towns where the virus was found in the sewage (25, 27). In particular, the stool survey in Rahat was conducted between July 2 and July 24, just before the start of the oral vaccination campaign, and included (after removing repeated samples of the same individual from within a 1-week span) a total of 546 samples of children under the age of 10, of which 26 (4.8%) were found to be positive for WPV (27).

Preprocessing of the data

Two criteria were applied to exclude cities or towns from the analysis before performing any calculations, as follows: (i) having insufficient measurements from that city or town; in particular, having fewer than four positive measurements between August 5 and September 30 and (ii) having a poorly defined catchment area with an overlap or spillage from neighboring sewage sources.

The data set analyzed included seven cities and towns (see Table 1 for further details) for the time period spanning August and September 2013, which captures 25% of the samples. Note that the remaining samples were spread over 68 different sites that were monitored less extensively; that is, merely ~2.1 samples per site (and that using just two data points per site in the mixed-effects regression below would have been highly problematic with regard to identification, etc.). During this period, more than 63,000 children below 10 years of age living in the combined sewage catchment area were vaccinated with the oral vaccine.

The vaccination data are in daily resolution, exhibiting a weekend effect (that is, the campaign was not conducted during the weekends; see Fig. 1); for the analysis, the vaccination data were summed to a weekly total, resulting in a similar temporal resolution to the sewage surveillance data. We analyzed the data from the initiation of the supplementary immunization campaign (August 5) until the conclusion of the first round of vaccination (September 30), just before the second round of vaccination was administered.

Data transformation

The first choice as a variance-stabilizing transformation of the number of persons vaccinated and the number of virus particles detected was the logarithmic transformation. The transformation handled well the many orders of magnitude that the data span. A fourth-order root transformation (and lower orders) was also tried but did not provide a major improvement to the model fit measured by R2; therefore, we retained the logarithmic transformation, which is also easier to interpret and more intuitive. As a result of choosing the logarithmic transformation, normalization with respect to the daily sewage volume production of each city or town was achieved by a simple addition or subtraction of its logarithm.

Statistical analysis

Mixed-effect models.

Preliminary analysis (see below) pointed to a strong relation between the number of people vaccinated 7 to 14 days before measurement and the number of plaque-forming units detected [see also (13), which found that the virus secretion during this period is much larger]; we therefore regressed the number of particles found on the number of people vaccinated 7 to 14 days before measurement. Simple linear regression and mixed-effects models (that is, allowing for a city-dependent intercept and a city-dependent slope) were fitted with R using the lme4 package (36). The first model examined was a simple linear model:Embedded Imagewhere y and x are the log of the number of particles detected and the log of the number of people vaccinated 7 to 14 days before, respectively, and ε is a normally distributed error term. The second model, a random intercept model, used the location of the measurement and assumed that each city or town has a different intercept term; that is:Embedded Imagewhere εc is a normally distributed, city-dependent unknown error term. The third model, a random intercept and random slope model, used the location of the measurement and assumed that each city or town has a different intercept term and a different slope term; that is:Embedded Imagewhere δc, a normally distributed error term, is fixed for each city or town.

Model selection.

The random intercept model was chosen for further analysis. This was because:

1) Examination of the AIC and BIC scores (37) of all three models (Table 2) provided strong evidence in favor of the random intercept model.

2) Notice that the logarithmic transformation implies that #particles =Embedded Image, where I is the number of individuals vaccinated. Thus, a random slope (particularly, a1 ≠ 1) implies that the number of particles detected will not scale linearly with the number of people secreting the virus, contrary to intuitive expectancy.

3) In accordance with (38), all three models yielded a1 ≈ 1 as expected, with little contribution due to random effects. Similarly, all three models yielded a0 ≈ 7.1 (however, with some contribution due to random effects, εc). Therefore, because model averaging (37) did not change the results substantially [because the leading weight, that of model (ii), is 84%, and moreover, a1 was very close to 1 in all three models], and to avoid the interpretation difficulties involved with model averaging, the results presented here are from the random intercept model.

Estimating the infection prevalence.

The motivation for the work presented here was to be able to use surveillance data from new locations to provide estimates of infection prevalence. Therefore, the roles of the independent variable [previously, the number of people (I)] and the dependent variable [previously, and mechanistically, the number of particles detected (S)] were switched. In other words, the (random intercept) regression is now: Embedded Image[see Table 3 (bottom) for the values of the estimated parameters].

To illustrate, we use the data collected in Rahat, the epicenter of the outbreak. A sewage sample of 0.5 liters immediately before the supplementary immunization campaign (5 August 2013) found 175 particles. We would expect to find 175 × 2000 particles per 1 m3 of sewage; further multiplying by the city’s sewage daily production volume (5200 m3/day), we obtained 109.26. Applying Eq. 1, with parameters given in Table 3, provided an estimate of 1663 shedders (95% CI, 360 to 7710).

Viral shedding is highest on days 7 to 14 after vaccination

We find that, as in (13), viral shedding peaked on days 7 to 14 after exposure (see Fig. 1 for an example from Beer-Sheva). This is in agreement with previous findings studying fecal samples from polio-challenged individuals (13). Although comparison with plaque-forming units is somewhat problematic, there is also some agreement between our evidence below, suggesting ~5 × 107 plaque-forming units per person per day (7 to 14 days after exposure), and the results of (13) estimating 1.3 × 105 TCID50 (50% tissue culture infective dose) per gram of feces, given that the relationship between TCID50 and plaque-forming units is about 1 plaque-forming unit = 0.56 TCID50 (39) [and the daily fecal production per person per day is 100 to 500 g (13)].

SUPPLEMENTARY MATERIALS

www.sciencetranslationalmedicine.org/cgi/content/full/9/383/eaaf6786/DC1

Materials and Methods

Fig. S1. Time courses of the number of vaccinated children and the number of polio particles detected in seven cities and towns.

Fig. S2. Relationship between viral particles detected and number of people vaccinated.

Fig. S3. Leave-one-out analysis.

Fig. S4. Histogram of residuals after regression.

Reference (40)

REFERENCES AND NOTES

  1. Acknowledgments: Funding: The authors state that they received no outside research funding for this work. Author contributions: Y.B., L.S.F., Y.M., A.H. and L.S.F. designed and performed all data analysis. Y.M., E.M., E.K., and I.G. collected the data. Y.B., and A.H. wrote the paper. Competing interests: The authors declare that they have no competing interests. Data and materials availability: Requests regarding the Israeli Ministry of Health data sets should be addressed to I.G.; all other requests should be directed to the corresponding author Y.B. Data are deposited in Dataverse with the accession number http://dx.doi.org/10.7910/DVN/9NDIRW.
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