Rubella is perhaps the infection for which mathematical modelling holds the greatest promise for improving public health interventions. The epidemiology is straightforward, and thus tractable to model development, but the effect of vaccination on the burden of disease is rooted in the nonlinearities of infectious disease dynamics. These dynamics are much studied, but here we explore them in a broader demographic and spatial context than previously. Across a global spectrum of demographic and epidemiological contexts, we show that the nonlinear epidemic dynamics of rubella can interact in complex ways with both birth rates and spatial heterogeneity to influence the consequences of vaccination.
To be useful, models must be rooted a realistic public health context, and deciding whether to introduce RCVs into the routine infant immunization schedule, and what additional vaccination strategies to use requires consideration of the financial and logistical feasibility of achieving and sustaining identified minimum coverage levels in all areas of the country, and indeed in neighbouring countries. Although the burden of CRS is small compared to the overall disease burden in children in certain regions, the low cost of the rubella vaccine and the ability to deliver it as a MR combination vaccine mean that it may be one of the diseases most effectively tackled. This is particularly true where regular measles SIAs continue with high campaign coverage. Switching from the measles vaccine to the MR vaccine entails an increase in cost – in 2010 the UNICEF discounted price per dose was US$0.8–1.50 for MMR and US$0.53 for MR, compared to US$0.22 for measles (http://www.unicef.org/supply/
) – but no additional resources would be required for distribution: the combined vaccine would simply be substituted for the monovalent vaccine. Furthermore, a Global Alliance for Vaccines and Immunizations (GAVI) support window for the rubella vaccine is in preparation for 2012 [14
However, rubella vaccine is also the only common vaccination whose use has the potential to lead to a negative outcome, i.e. increased incidence of CRS. We found that in the simplest analysis, where population sizes are large enough that stochastic effects can be ignored, introduction of routine infant and young children rubella vaccination once coverage is sustainable at
80% is conservative under many demographic and transmission conditions, particularly when birth rates are <30/1000 (), in line with previous work [5
]. However, necessary vaccination coverage increases strongly with birth rate, and this coverage level is insufficient for routine vaccination alone in countries where the birth rate is >30/1000 and the basic reproductive rate of rubella is >8. Starting (‘catch-up’) campaigns followed by regular high-quality SIAs () lowers the requirement for coverage across birth rates, as long as SIAs reach children who were missed by the routine programme and in the absence of stochastic effects (see below). Results are conservative relative to mixing assumptions (Fig. S5) and robust to the assumption of stable populations (Fig. S7).
Vaccination of women of childbearing age is the one strategy that will always improve the CRS situation. While such targeted campaigns should play an important role in a rubella control strategy, they face several logistical hurdles. Significantly, such a campaign could not be paired with existing measles control programmes, and thus would require a major investment in a vaccination programme aimed solely at the control of rubella. Additionally, identifying women in need of vaccination may be difficult. Overall, whether the benefits of pursuing rubella vaccination of women of childbearing age outweighs the costs will depend on coverage and the age profile of access to vaccination. In our analyses, we set a gradually increasing pattern of access to vaccination with age (Fig. S1e), and coverage equivalent to half that achieved in routine vaccination. This may be conservative: WHO reports 75% coverage for tetanus toxoid immunization, a vaccination targeted at pregnant women via routine programmes. However, vaccination of pregnant women is unlikely to be implemented for rubella and it is unclear if similar rates of success could be reached across populations.
The effect of seasonal forcing on CRS burden has not previously been addressed. Motivated by recent results highlighting both its amplitude and importance for measles dynamics in a Sahelian context [23
], we explored seasonal forcing in detail here. Our results suggest that seasonality is rather negligible relative to effects of birth rate (Fig. S5). Rubella does frequently display multi-annual cycles [35
], which could affect the age profile of infection [24
]. Transient dynamics interacting with seasonal forcing has been proposed as the mechanism [11
], rather than strong seasonal forcing per se
]. Such effects may only shift the age of infection up by a small amount [21
], and are thereby unlikely to affect the burden of CRS, but their existence (e.g. [11
]) implies that stochasticity is an important element of the dynamics of rubella.
If stochasticity is important, the generally positive situation for vaccination depicted by the deterministic analysis here and elsewhere [5
] needs to be interpreted cautiously in a world of heterogeneous vaccination rates. Local extinction might dominate rubella dynamics (e.g. see data from Peru [22
] and early data from The Gambia [37
]). This will allow build-up of susceptible individuals in older age groups (demonstrated for remote areas in Peru [22
]) increasing the burden of CRS and potentially altering the outcomes of vaccination. Our stochastic analysis highlights that risks are high if vaccination is introduced in one location (country or community) and there is substantial cross-migration with unvaccinated communities where rubella circulation is maintained by imports. These results echo those of Vynnycky et al
] in that inequality in access to private-sector rubella vaccination when it is not available in the public sector may affect the CRS burden. Note that these results will also be sensitive to the assumptions of the exact generation time of the infection, as well as the value of the exponent γ (since values closer to 1 lead to more violent dynamics more prone to extinction) and for quantitative predictions these should be carefully estimated.
Our model makes several assumptions. We assumed that a person's chance of being vaccinated in an SIA is independent of their probability of routine vaccination and vaccination in previous SIAs. However, those children not covered by routine vaccination may have been missed for some reason that increases their likelihood of being missed by SIAs, leading to a systematically unvaccinated population. Recent work has shown that this group may represent as much as 20% of the population in some countries [38
]. The existence of such a group will cause us to overestimate the benefit of SIAs; hence we urge caution in the interpretation of our results and suggest that the estimated coverage of SIAs be ‘discounted’ and accordingly considered to be up to 20% lower if such an unreachable population is believed to exist. This is a key area for future work on specific contexts. We assumed that seasonal forcing followed a sinusoidal pattern (Fig. S1b). More realistic patterns may alter the range of multi-annual cycles [10
] and could influence our conclusions on the weak effect of the magnitude of seasonal forcing on vaccination outcomes; time-series data at sub-annual time-scales would be required to investigate this. Our model is likely to be robust towards biases from other assumptions; and where biases exist, the model will tend to be conservative, overestimating rather than underestimating the minimum required coverage. For example, we assumed approximately 24 rubella generations per year; in fact there may be slightly fewer, since rubella has a generation time of about 18 days [5
], implying that our model slightly overestimates yearly transmission rates, thus over-predicting minimum required levels of vaccination; sensitivity analyses suggest that this will have little impact over much of the range of vaccination (Fig. S2), but should be borne in mind for highest coverage levels. We assumed constant survival rates over age, which will result in an exponential distribution of the population over age, and may underestimate the relative proportion of women of childbearing age, and thus the CRS burden, particularly in populations where birth rates are lower (e.g. Europe). However, repeating the analysis with empirically based age trajectories of survival reflecting the likely range of age trajectories of survival which results in non-stationary populations (either growing or shrinking, depending on the balance of mortality and birth rate) does not much alter required minimum vaccination coverage (Fig. S7). Finally, we assumed that transmission is constant over age. If transmission is more clustered in younger age groups, as has been reported from surveys of contact patterns over age in European countries (Fig. S2b) the necessary vaccination coverage is higher (Fig. S8), particularly at lower birth and transmission rates (albeit retaining general patterns relative to the 80% threshold); however, the absolute number of CRS cases will be much smaller than is estimated with constant transmission over age (Fig. S9), as will be the increase driven by insufficient vaccination. Specific data needs for improved predictions relative to the various assumptions are detailed in Supplementary Information S3.
Overall, our results have several implications for introduction of RCV. First, declining birth rates in low- and middle-income countries raise the priority for rubella vaccination because; (i) falling birth rates increase the average age at infection, thus increasing the burden of CRS in the absence of vaccination, and (ii) the critical vaccination coverage required to reduce CRS incidence will be lower at lower birth rates, increasing the chances of a successful vaccination programme [36
]. Second, given the current global range of birth rates, in all regions except Africa, if routine infant and young children measles vaccination coverage is
80% it is likely to be safe to switch to MR combined vaccines, in the absence of major heterogeneities in coverage, particularly as birth rates fall. Substantial programmatic efforts would be needed in large countries such as India; however, to avoid potential increases in CRS that could occur through spatial dynamic effects on transmission if the substantial heterogeneity in coverage that has been seen for measles vaccine (with up to fourfold differences in coverage between states) continued. Third, private-sector vaccination against rubella should be monitored as much as possible, to assess whether private-sector coverage has reached levels sufficient to increase CRS burdens (), and if so, national introduction policies should be considered. Fourth, in the African region, where birth rates remain >40/1000 in many countries and estimates of R0
are >6 [18
], infant and children vaccination alone should be considered with caution and SIAs would be essential as long as birth rates remain high. Even with SIAs, the potential for spikes in CRS incidence to occur in the short term implies the need for effective communication to avoid public mistrust of the programme. Fifth, the addition of vaccination of women of childbearing age has the potential to greatly enhance programme effectiveness and reduce risks of increases in CRS. Finally, the potential for local extinction and delayed outbreaks should be a factor when considering implementing any of the above recommendations. In the WHO African and South-East Asian regions, the only regions where universal rubella vaccination is currently uncommon [3
], it would be prudent for changes in rubella vaccine policy to be taken at regional level rather than by individual countries, and for introduction of RCVs to be accompanied by intensified efforts to reduce heterogeneities in routine vaccination and SIA coverage.
The public health recommendations above are developed in the context of rubella, but the results of our analysis also provide a global overview of the degree to which complex feedback between key drivers inherent in infectious disease dynamics shape infection, and are therefore important to consider for successful control. Our broad analysis of the effects of seasonality, spatial coupling, and stochastic effects on both incidence and the age profile of incidence provide a global scale overview of the landscape of the dynamics of such infections, key for assessing safe and effective implementation of control strategies.