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  • The number of people infected with Sabin polioviruses is primarily determined by the number of doses of OPV administered during routine and supplementary immunisation activities and the level of population immunity. As the amount of OPV administered increases from zero, the number of Sabin-infected individuals will initially increase, but at some point further increases in OPV administration are likely to result in a decrease in the number of individuals infected because of the associated increase in the level of population immunity. This implies a trade-off in the levels of OPV use that will favour VDPV emergence. We developed two mathematical models to study this trade-off: an analytical model that includes only SIAs, and a more complex model that includes both routine immunisation and SIAs, which must be solved through numerical simulation. We used these models to investigate the risks and benefits of carrying out preventive campaigns with tOPV as a strategy to maximise population immunity to serotype 2 prior to OPV2 withdrawal. We assume that a proportion of the population s0 is susceptible at the time that SIAs commence. We also assume that the SIAs occur at least 4 weeks apart but in sufficiently close succession such that we can ignore births and deaths during the period of analysis. Under these assumptions the expected proportion of children shedding vaccine poliovirus after a single SIA i1 can be written i1=y11+y21(1) where y11 is the proportion shedding as a result of direct administration of OPV during the SIA and y21 the proportion shedding as a result of secondary spread of OPV from that SIA (i.e. y11 and y21 differ on the source from which the infection is acquired, the vaccine or a Sabin-infected individual). We denote the coverage of the campaign by v, vaccine “take” by w, and the basic reproduction number of Sabin polioviruses by R0S. We assume all individuals who shed poliovirus following vaccine “take” are subsequently immune to reinfection and do not thereafter participate in poliovirus transmission. The expected proportion of children shedding following direct administration of OPV is then given by y11=s0vw(2) assuming in this simple model that immunised individuals cannot be reinfected with OPV. The expected proportion of children who subsequently shed as a result of secondary transmission of OPV under a simple SIR model satisfies y21=(s0−y11)[1−exp(−R0S(y11+y21))](3) following Bailey 1975 [17], where s0−y11 is the proportion of children susceptible to infection. Note that secondary spread of OPV includes second, third and subsequent generation spread, and not only transmission from a vaccinated individual. Following this SIA, the proportion of the population that is susceptible is reduced by i1 such that the fraction susceptible becomes s1 = s0−i1. We assume that all secondary transmission has finished before the next SIA. This is a reasonable assumption if R0S < 1 because the majority of secondary transmission will take place in under 4 weeks (Section A.1.1 in S1 Text). Subsequent SIAs are assumed to reach the same proportion v of the population (i.e. same coverage), which may either consist of randomly chosen individuals at each round (random coverage) or repeatedly reach the same fixed group of individuals (fixed coverage), meaning there is a persistently “missed” group. Each of the subsequent n SIAs will result in the proportions i2,i3,…,in of individuals shedding Sabin poliovirus, and s2,s3,…,sn susceptible (see Section A.1.2 in S1 Text for modelling details under the two types of SIA coverage, random and fixed). The number r of emergent VDPVs following the n SIAs can be considered a function of the number of individuals infected with Sabin poliovirus. The probability of Sabin reversion to VDPV may differ by whether the infection is primary or secondarily transmitted. In the simplest case, we assume all Sabin infections have the same, very small probability of reverting to a VDPV. In this case, the number of emergent VDPVs is given by r≃ρN∑k=1nik(4) where N is the total population size and ρ is an unknown parameter that determines the absolute risk of VDPV emergence (i.e. reversion of a Sabin virus). The latter is assumed to capture unknown risk factors such as the prevalence of other enterovirus serotypes that could act as partners for recombination and the prevalence of primary immunodeficiencies that might result in prolonged excretion of vaccine poliovirus. Because the number of emergent VDPVs depends on ρ and N via their product, we can reparameterize r by introducing the parameter σ = ρN: r≃σ∑k=1nik(5) The probability that an emergent VDPV spreads and produces one or more AFP cases will depend on the size of the resulting outbreak. The cVDPVs characterised so far appear to show similar attack rates to wild poliovirus [8,12] and are therefore likely to have a reproduction number R0V sufficient to result in a significant outbreak unless population immunity levels are high. The probability of an outbreak of VDPV for a simple epidemic model is given by q = max(1−1/(R0Vs),0), where s is the proportion of the population susceptible to infection. For a major outbreak, the duration of transmission will significantly exceed 4 weeks (unlike Sabin virus) and therefore we make the assumption that s ≈ sn, i.e. population susceptibility is defined at the end of all n SIAs. Assuming the overall risk of emergence is relatively small, this means that the number of emergent VDPVs that will produce an outbreak will be approximately Poisson distributed with mean proportional to rq. The probability of (at least) one outbreak of VDPV occurring is therefore given by P(VDPV outbreak)=1−exp(−rq)(6) and the expected proportion of individuals that have been infected with a VDPV once the outbreak has finished can be obtained using the equation for y21 and replacing R0S by R0V, s0−y11 by sn and y11 by ρ∑k=1nik. Fig A in S1 Text illustrates the processes captured by this model. We use this model to explore how the probability of a VDPV outbreak changes for different number of SIAs and different SIA coverage in a scenario without routine immunisation. The model of Sabin virus spread during the n SIAs described above can be reformulated (Section A.2.1 in S1 Text) and using this equivalent version, some system’s properties can be studied analytically, leading to a more general understanding of the model’s behaviour. Very briefly, we show that multiple rounds of SIAs with the same coverage v are equivalent (in terms of the proportion of individuals infected with Sabin at some point and the proportion who remains susceptible after the SIAs) to a single round of SIA with vaccine coverage given as a certain function of v, w and n. For interested readers, the equivalent version of the model and the analytical results that can be obtained are given in Section A.2 in S1 Text. Stochastic compartmental model: routine immunisation and SIAs: We wish to study the risk of VDPV emergence and spread in the context of OPV withdrawal. It is thus necessary to extend our previous conceptual framework to include routine immunisation. In order to include both routine and supplementary immunisation, we constructed a stochastic compartmental model of Sabin virus and VDPV spread that also considers births and deaths. If a fixed proportion of individuals vri is reached by routine immunisation at each scheduled dose, and three doses of OPV are given, then assuming that only a fraction w of those doses will “take”, the proportion c of children who received the three doses and shed Sabin virus is c = vriw(1+(1−w)+(1−w)2). We model secondary spread of OPV through an SIR model with demography where the proportion c of children vaccinated and shedding the virus enter the model as infected with Sabin poliovirus, and the other children enter the model as susceptible. As before, a small proportion ρ of incident Sabin poliovirus infections are assumed to revert to VDPV, which may then spread in the population. In this simple case, we assume that this proportion is fixed and independent of whether infection was acquired directly through immunisation or through secondary spread of OPV. See Section A.3 in S1 Text for the full model description. As for the analytical model above, two versions of the stochastic model were implemented: one where each SIA reaches a fixed proportion of the population consisting of randomly chosen individuals at each round (random coverage, Table A in S1 Text), and one where the same individuals are reached at each SIA, thus leaving a persistently “missed” group (fixed coverage, Table B in S1 Text). We used the model to explore how the risk of VDPV2 emergence and spread varies depending on tOPV use in a context of OPV2 withdrawal and considering a population of 10,000 individuals. We simulated the model from a VDPV2-free initial equilibrium for 1 year under different scenarios that included different levels of routine immunisation coverage and between 0 and 5 SIAs (Fig 1). Routine immunisation with tOPV was assumed to stop at 6 months and the last tOPV SIA 4 weeks before this date corresponding to plans for SIAs with tOPV before OPV2 withdrawal. We defined the risk of a VDPV2 outbreak after OPV2 withdrawal as the probability of having >200 incident VDPV2 infections during the 6 months following OPV2 withdrawal (robustness of this threshold for increasing population size is explored, Fig F in S1 Text). This corresponds to a probability of approximately 20% of observing a case of poliomyelitis, given a case-to-infection ratio for serotype 2 of approximately 1:800 (based on data indicating 4–5 times lower pathogenicity for this serotype compared with serotype 1 [18], which has a case-to-infection ratio of about 1:150 [19,20]). We performed 500 simulations for each scenario and present the proportion of simulations that resulted in this outcome. Figure data removed from full text. Figure identifier and caption: 10.1371/journal.ppat.1005728.g001 Illustration of results from the stochastic dynamic mathematical model of VDPV2 emergence and spread.The model is simulated for 1 year and a population of 10,000 individuals, starting from a VDPV-free equilibrium that includes routine immunisation. OPV2 withdrawal occurs at 6 months (red arrow) and the last tOPV SIA is assumed to occur 4 weeks before this date in agreement with current plans. SIAs are implemented 4 weeks apart. We define the risk of a VDPV2 outbreak after OPV2 withdrawal as the probability of having >200 incident VDPV2 infections during the 6 months following OPV2 cessation. In this illustration, the grey lines represent the number of VDPV infected individuals over time for 20 different simulations of the model assuming 20% routine immunisation coverage and 3 tOPV SIAs with 80% coverage implemented before OPV2 withdrawal. For both models (the SIA-analytical and the stochastic dynamic), the probability of vaccine “take” was set at w = 0.55 [21] and the reproduction number of Sabin virus was assumed to be <1 and fixed to R0S = 0.5. The reproduction number of VDPVs was set at R0V = 5, similar to estimated values for wild poliovirus [22]. Finally, the probability of Sabin virus reversion to VDPVs was set at ρ = 5×10−4, although we explored sensitivity of our results to this value. Risk factors for VDPV2 emergence and spread in Nigeria (2004−2014): Multiple emergences of VDPV2 were identified in Nigeria during 2004−2014 on the basis of detection of virus in stool collected from children with AFP and phylogenetic analysis of the P1/capsid region [15,23]. We recorded the district of residence and date of onset of paralysis for the first case of AFP associated with each of these independent emergences. We created a database for all the districts of Nigeria for the period 2004−2014 that included variables describing routine immunisation coverage, serotype-2 population immunity, the number of tOPV SIAs in the preceding 6 months (since VDPV2 emergence will precede detection in a child with AFP by about this time period, based on observed genetic divergence from the Sabin virus [23,24]), and demographic variables including mean household size, population density and annual number of births (Section B in S1 Text). We compiled the data for 6-month periods, defined as April-September and October-March (roughly corresponding with a high-transmission period during spring-summer months and a low-transmission period in autumn-winter months). This resulted in 772x19 = 14,668 district 6-month observations (from April 2004 to September 2014). Serotype-2 population immunity was estimated among children 0–2 years old based on the vaccination histories of children with non-polio AFP and the SIA calendar (Section C in S1 Text). Routine immunisation coverage was estimated interpolating data across the whole country for three doses of diphtheria-tetanus-pertussis (DTP3) vaccination from the Demographic and Health Surveys (DHS) [25] clusters (Section D in S1 Text). We used a “case-control” approach to compare districts in a given 6-month period where VDPV2 emergences occurred with districts in a given 6-month period where there were no VDPV2 emergences. In this framework, a “case” was defined as a district over a 6-month period (district−6-months) where the first AFP case associated with a VDPV2 emergence was detected. A “control” was defined as a district−6-months with no VDPV2 emergences. Each district−6-months case was matched to 20 district−6-months controls from the same 6-month period to allow for potential confounding as a result of secular trends. The controls were randomly selected among all the district−6-months candidates that satisfied the matching criteria (i.e. same 6-month period). We performed univariable and multivariable analyses using conditional logistic regression models. Odds ratios (ORs) and 95% confidence intervals (CIs) were calculated for all explanatory variables and associations with P values <0.05 were considered to be statistically significant. All variables with Wald test P <0.05 in univariable analyses were included in the multivariable models and the final multivariable model was the one with the lowest AIC [26]. All the analyses were performed using the “survival” package [27] from R [28]. Finally, we also used univariable logistic regression analyses to test whether any of the variables were associated with the probability that a VDPV2 emergence resulted in >1 case of poliomyelitis (i.e. established a circulating lineage), thus corresponding to the definition of cVDPV used until July 2015, which required that genetically linked VDPVs were isolated from at least two AFP cases.
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