Our results reveal several interesting discrepant findings among the model projections for the short- and long-term impact of vaccination that shed light on some of the important questions about rotavirus epidemiology. Direct comparison of differences in model structure and estimated parameters allows us to understand the reasons for the variation in model projections. Fundamentally, these variations in model projections reflect gaps in our understanding of the mechanisms of rotavirus infection, natural immunity, epidemiology, and the biological nature of vaccine protection. Much of the uncertainty regarding the expected indirect effects of vaccination in the literature stems from different model assumptions for why severe RVGE is rare among older children and adults, and to what extent natural and vaccine-induced immunity wanes over time.
The five models we analyzed reproduce the seasonality and age distribution of rotavirus incidence in E&W, providing an important source of model validation. We compared the statistical fit of these models to week- and age-stratified laboratory reports of confirmed rotavirus cases from E&W, and found that all five models had AIC values between 66,697 and 84,997. Given the large number of data points we attempted to fit (547 weeks×19 age groups
10,393 data points), the relatively large AIC values and the variation among models with different numbers of estimated parameters is not surprising. Model E provided the best fit to the pre-vaccination E&W RVGE reports, but the relative ranking of models based on AIC should be interpreted cautiously when extrapolating to the ability of the models to predict the impact of vaccination. Furthermore, we only explored a single set of fixed parameters and fit to a single data set; there is additional uncertainty regarding the parameter values that was not accounted for in our analysis, and which would presumably affect the fit differently for different models.
The models make different assumptions to explain why most RVGE cases occur among children <5 years of age (). Both Models A and D allow for the risk of infection and/or reporting to vary by age, and both models find that older individuals are less likely to be infected with rotavirus than younger individuals given equal levels of exposure (except among ≥65 year olds in Model A) (). These models are characterized by lower estimated values of the basic reproductive number R0 (quantifying the transmission potential of rotavirus), suggesting that the high incidence of rotavirus infection in the population is due to the repeated infection of individuals throughout their lifetime rather than being due to the large number of individuals who can be infected by a single individual with a primary infection. However, Models A and D differ in that Model A assumes that individuals ≥5 years of age are less prone to severe RVGE than those <5 years of age and therefore tend to be less infectious, whereas Model D assumes that severe infections occur in older individuals but tend to be under-reported at a higher rate. Furthermore, Model A assumes that immunity following natural infection and vaccination is not long-lasting and that the decline in the proportion of cases in older age groups is entirely due to age-specific differences in the risk of infection and disease. Model D assumes that immunity gained through repeated natural infections partially accounts for the greater concentration of RVGE in younger individuals. While Model A does not track asymptomatic infections and assumes they play no role in transmission, Model D does take into account possible transmission from such infections. Together, these differences help explain why the R0 for Model D is slightly greater than the R0 for Model A.
Models B, C, and E are similar to Model D in that they also assume the progressive build-up of natural immunity to both infection and symptoms of infection explains the greater concentration of RVGE in children <5 years of age. Immunity is assumed to wane on a time scale that does not affect the <5 year old population (). Unlike Model D, however, these models do not allow the rate of reporting of RVGE to differ between the <5 years old and ≥5 years old age groups. Thus, the estimated values of R0 for these models tend to be higher, suggesting a higher incidence rate of infection and younger age of first infection with rotavirus. As a result, there should be a greater correlation between the age distribution of reported RVGE cases and the RVGE cases responsible for the majority of rotavirus transmission predicted by Models B, C, and E. In contrast, Model D implicitly assumes that unreported cases of RVGE in older children and adults play an important role in transmission; paradoxically, this model projects stronger indirect protection because there are fewer overall infections among older individuals in Model D than in Models B, C, and E. In essence, Models A and D place more emphasis on adults in the transmission process compared with Models B, C, and E.
Part of the difficulty in deciding which model best represents the underlying epidemiology of rotavirus infection is lack of knowledge about the reporting pyramid for rotavirus. In other words, what fraction of rotavirus infections are symptomatic, what fraction of symptomatic infections present to the healthcare system, and what fraction of those presenting get properly diagnosed as rotavirus? A few studies have attempted to elucidate the reporting pyramid for rotavirus infections in E&W, but they were underpowered to understand the reporting fraction in adults, how reporting varies over time, and how it correlates with the severity of symptoms 
The similarities and differences in model structure are reflected in the projections that each model yields for the indirect protection conferred by vaccination. During the first 5 years after vaccine introduction, the reduction in the cumulative incidence of severe RVGE predicted by each model was similar for children <5 years of age and for the overall population. However, it is more difficult to predict the pattern of epidemics following the introduction of vaccination, as suggested by the different epidemic trajectories predicted by each model. Furthermore, none of the models account for additional complexities such as the interaction among different genotypes of rotavirus, or environmental or local effects. All of the models suggest that the post-vaccination timing of rotavirus activity can vary considerably, with possible peaks occurring in the summer and/or fall as opposed to the typical pre-vaccination peaks occurring in winter/spring. This is consistent with the relatively low amplitude of seasonal forcing (4.3–6.4%) estimated for each model, which suggests that environmental factors such as temperature or humidity only have a small effect on the transmission rate, and that the large RVGE epidemics evident in E&W primarily result from the dynamic interaction between susceptible and infectious individuals 
. By altering the rate at which fully susceptible infants enter the population, vaccination can lead to significant changes in the timing of rotavirus activity; thus, models of the transmission dynamics of rotavirus can aid in our understanding of the observed incidence patterns 
Model projections suggest the short-term reduction in the incidence of reported RVGE during the first five years after vaccine introduction will exceed estimates that account only for the direct effects of vaccination. This is supported by recent observations of the early impact of vaccination in countries that have introduced routine immunization, where 22–68% decreases in the incidence of RVGE have been reported in age groups not eligible to receive the vaccine 
, including older children and adults 
. At three sentinel sites in the US, the overall incidence of hospitalization for RVGE among children 6–11 months of age was reduced by 87% in 2008, when coverage among this age group was 77%; but in 2009 the RVGE hospitalization rate among <3 year olds was similar to that expected based on coverage and vaccine effectiveness estimates 
. Models B, C, and E predict that the indirect benefits of vaccination during the short term may not extend to the long term, as the burden of RVGE may shift to older age groups. Beginning in the second year after vaccine introduction and continuing to the long term, model projections differ considerably for the ≥5 year old population.
All of the models predict that vaccination will lead to a delay in the average age of first infection with rotavirus and a decrease in the number of infections experienced by a single individual during his/her lifetime (results not shown). For Models B, C, and E which assume that the severity of RVGE is associated only with the number of previous infections, the delay in the time to infection may shift some of the burden of severe RVGE to older individuals, because first and second infections may be more likely to occur after 5 years of age. If infections tend to be less severe and/or less likely to be reported in the ≥5 year old age group than in the <5 year old group, as estimated by Models A and D, the delay in the time to infection is not predicted to increase the burden of RVGE in the ≥5 year old age group. Furthermore, the decrease in the overall number of infections experienced by individuals during their lifetime could translate into a decrease in the number of severe RVGE cases among older individuals, particularly if the lifetime number of infections predicted by the model is relatively small.
Whether or not vaccination provides long-term indirect protection against severe RVGE in children <5 years of age depends on whether vaccine-induced immunity wanes completely after 1 year, or if vaccinated infants remain at reduced risk of RVGE for a prolonged period of time. The discrepancy in results between Model A, which predicts the smallest reduction in severe RVGE, and Model D, which predicts that elimination of RVGE is possible under some scenarios, is due primarily to the different assumptions made regarding the duration of immunity. If one makes the alternative assumption in Model A that vaccine-induced immunity lasts at least 3 years, then in this case Model A also predicts that rotavirus could be eliminated at high coverage rates 
. Models B and C assume that the effect of vaccination may wane partially after 1 year, but that vaccine-induced immunity does not wane completely, whereas Model E assumes that long-lasting immunity is only generated in some individuals. Determining if vaccine-induced immunity wanes over time, how waning occurs, and how it differs across populations, is an important avenue for future research.
An important limitation of this study is that we do not comprehensively explore the influences of parameter uncertainty. Key uncertainties in our fixed parameter assumptions for rotavirus include the duration of natural and vaccine-induced immunity, protection conferred by previous infection(s), and relative infectiousness of primary and subsequent symptomatic and asymptomatic) infections. Further work is needed to characterize and explore the impact of this parameter uncertainty 
, while epidemiologic studies are needed to obtain better estimates of unknown parameters.
Overall, the comparison of these different models of rotavirus transmission and vaccination allowed us to examine the impact of structural uncertainty on the robustness of model projections, as well as identify key gaps in our understanding of rotavirus epidemiology. The models we compared suggest vaccination will lead to a 64–100% reduction in the incidence of severe RVGE and a 55–100% reduction in any RVGE at full coverage 10–20 years following vaccine introduction if vaccination confers protection comparable to a single natural infection (, Figure S3
). Similarly, vaccination will result in a 78–100% reduction in severe RVGE and a 70–100% reduction in any RVGE if a second dose of vaccine confers additional protection. How the reduction in the incidence of severe and any RVGE translates to fewer cases of reported RVGE will depend on whether reporting reflects only cases of severe RVGE or both mild and severe RVGE. Indirect protection against RVGE apparent in the first few years after vaccine introduction may or may not extend to the long term. Whether it is possible to eliminate rotavirus infection from the population depends critically on the transmissibility of primary infections (as indicated by the estimated R0
of the best-fit models), what fraction of cases goes unreported, and whether immunity wanes over time.
Our comparative analysis of the model projections for the indirect effects of vaccination identified three key questions that should be addressed to improve the accuracy of model predictions:
- What is the role of adults in rotavirus transmission? Infection with rotavirus later in life is typically asymptomatic and/or unreported, but infected individuals could be transmitting rotavirus to others. The models we explored differed in the emphasis placed on transmission from older children and adults, which could account for some of the differences in projections of the long-term impact of vaccination.
- What is the effect of multiple vaccine doses on protection? Vaccination appears to confer immunity similar to that of natural infection, but it is unclear whether multiple doses of the vaccine yield an added benefit. We explored a variety of different assumptions regarding the impact of multiple vaccine doses, and found that the indirect benefits of vaccination may be greater if each dose confers immunity comparable to an additional natural infection. Understanding whether additional doses of vaccine provide additional protection could lead to new dosing schedules for developing countries, where vaccine efficacy is lower.
- Does vaccine-induced immunity wane over time? If so, what is the nature of this waning of immunity, i.e. is it complete or incomplete? The models we explored make different assumptions about the possible waning of immunity, from complete waning of vaccine-induced immunity to no waning of immunity. Age-specific estimates of vaccine efficacy and case-control studies of vaccine effectiveness during the second year of life suggest that there may be some waning of vaccine-induced immunity , , , , particularly in developing country settings , , , , but interpretation of this data is complicated.
Experimental studies of rotavirus pathogenesis, carefully designed epidemiologic studies, and stronger statistical links between data and models will lead to better-informed model assumptions and help to discriminate among models. In addition, further validation and fitting of transmission dynamic models to post-vaccination data from different countries will help to refine model parameter estimates and improve projections of the long-term impact of vaccination.