This modeling study demonstrates that the phenomenon of reduced rotavirus vaccine efficacy in low SES can be explained by intrinsic immunological and epidemiological factors. While natural rotavirus infections protect against subsequent infections across a range of SES, a key difference is that, unlike in middle and high SES, in low SES the proportion of infections that result in symptomatic disease does not rapidly decline with each subsequent infection; a similar proportion of primary or secondary infections result in severe rotavirus disease when compared with tertiary and subsequent infections. Thus, if vaccination mimics primary and/or secondary natural infection(s), subsequent infections and illnesses will not be adequately protected against, resulting in lower VE and shorter apparent duration of protection in low SES where subsequent infections occur at a high rate and continue to be severe.
A number of model VE outputs, predicted based on the natural history and immunogenicity data, are consistent with clinical trial findings, which is reassuring regarding the validity of our assumptions. First and foremost, the model predicts higher VE with increasing SES. Efficacy against severe RV-GE was similar in our model (93%) as it was for RV1 and RV5 in clinical trials and observational studied in high SES, where VE of greater than 90% was observed. 
Similar effectiveness estimates have been found in post-marketing surveillance studies. 
Our estimate of 86% efficacy against severe RV-GE in middle income countries is again consistent with trials across Latin America (83%), in South Africa (77%), and Vietnam (72%), and observational studies of effectiveness in El Salvador (76%) and Brazil (76%). 
Our VE estimate of 51% in low SES populations approximates the VE of 49% in Malawi, 43% in Bangladesh, and 39% observed in three sub-Saharan African countries. 
Our main results relied on the mean seroconversion rates by SES. However, in limited sensitivity analysis, we demonstrated that the range of seroconversion rates observed in immunogenicity studies may also explain some of the variation in VE from clinical trials.
Secondly, the model projects VE against severe RV-GE to be approximately 25% greater than against all RV-GE in middle and high SES. This is remarkably consistent with trial data from high SES. 
However, the model does not predict this differential efficacy in low SES because the proportion of cases that are severe is similar with each subsequent infection. The limited data from these settings indicates that the gap between severe and all RV-GE VE may be smaller. 
If future data on all-severity RV-GE in low SES support this prediction, it will give further support to the notion that the mechanism of vaccine action is to mimic natural infection, as well as helping to understand the potential impact of the vaccine on transmission in these settings.
Third, the model predicts and provides an explanation for what appears to be ‘waning’ of VE in low SES but not high SES populations, which has been observed in the clinical trial data. In 3 African settings, efficacy of RV5 against severe RV-GE was estimated to be 64% in the first year of life, falling to 20% in the second year 
; smaller, but nonetheless important declines have been observed in El Salvador, Nicaragua and Brazil, 
though it should be noted that studies have generally not been powered to estimate effectiveness in second year of life and beyond. The model does not fully capture how quickly VE falls; in clinical trials, VE declined by the second year of life and in the model, it fell in the third. However, waning – traditionally defined as loss of immunity over time – is not an influential feature of the model (as waning occurs on a scale of >40 years). Even without loss of immunity, VE as measured by clinical trials or cohort studies, can, in some circumstances, fall with increasing age. If vaccination reduces the force of infection and provides only partial protection for vaccinated individuals, proportionally more cases will occur in older age groups amongst vaccinated than unvaccinated individuals. 
Still, a better model fit could perhaps be achieved by explicitly incorporating loss of immunity, in effect representing local versus systemic immunity. However, the data needed to parameterize such a model for a range of SES are not available.
Because immunity to rotavirus is incrementally-acquired, our model proposes a different mechanism to explain reduced VE in older children. In the model, each dose of the vaccine mimics a natural infection. With a two-dose course, all children who respond to vaccination in higher SES are protected against severe disease as all severe disease is thought to occur as a result of the first two infections. In low SES, the mechanism of the vaccine is the same and higher order infections do confer additional protection against infection 
, but severe disease continues to occur in third, fourth and subsequent infections. These higher order infections make up a larger proportion of infections as children age, and are not protected against by vaccination, so in older children VE appears to ‘wane’. This is an important observation in that it suggests that additional vaccinations, for example a dose given with measles vaccination in the EPI schedule at 9 or 12 months, may improve performance among children in low SES, although the level of protection conferred by such schedules needs to be clinically evaluated.
We have assumed that the immune response to natural infection and vaccination, immunogenicity of vaccines, and background rotavirus incidence are independent factors, and this may be an important limitation. For example, part of the reason that live oral vaccines may be less effective is due to concomitant infections of the gut, as had been posited for OPV. 
Rotavirus and other concomitant infections will both be more common in low SES/high incidence settings, where vaccines also appear to be less immunogenic. 
As we have demonstrated, background rotavirus incidence itself may affect the impact of the vaccine program, but not VE directly; concomitant infections could still explain lower VE by interfering with both the immune response to vaccination and immunogenicity of vaccines.
We have also assumed that the severity of disease is dependent on the number of previous infections (and decreases with each subsequent one). However, it remains possible that severity is age-dependent. If, for instance, under 1 year-olds are more susceptible to severe disease regardless of the number of previous infections, just delaying age at infection will reduce severe disease. Age and number of previous infections may confound each other, but due to limitations in available data it is difficult to disentangle these factors. It is important to note that the younger age distribution of infection in low SES may at least partly explain the discrepancy in natural immunity between mid/high and low SES. Research directed at this issue may help to elucidate the extent to which simply delaying time to infection could result in a reduction in severe disease.
We are not aware of any robust data on mixing patterns and contact structures for either middle or low income settings, so we assumed mixing was proportional to age-specific patterns for Great Britain from a large European study. 
These data are unlikely to represent mixing patterns in either Mexico or India. We account for this, at least in part, by allowing the parameter q
to vary. q
represents the probability of transmission given a contact between a susceptible and infectious person. However, q
may also be interpreted as a composite of infectiousness and frequency of contact, so a higher q
ultimately represents a higher force of infection, which could result from greater infectiousness or more frequent contacts. Further studies are needed to elucidate mixing patterns for middle and low income settings.
Underpinning our results are the findings from the Indian natural history study that severe disease continues to occur in third and subsequent infections, whereas in Mexico severe cases are principally restricted to primary infection. A host of reasons for this discrepancy are possible. Exposure to higher doses of virus may occur in low SES, which could overcome immunity from previous infections. Greater strain diversity and more limited cross-protective immunity may also play a role. In addition to the mechanism we have modeled, immunity from both natural infection and vaccination may wane (in the “traditional” sense), whereby protective antibody is lost over time in children in low SES.
We have taken data from the UK, Mexico and India to be a general reference for the diverse range of epidemiological and demographic profiles of high, middle and low SES worldwide. Clearly, this is a simplification as factors such as crowding and underlying rates of diarrhea differ both between and within countries such as India, resulting in lower VE. 
Despite this simplification, we were able to match many of the observations of rotavirus vaccine clinical trials, suggesting that this framework is a useful tool for understanding some of the variation in VE across populations.
Our results help identify potential strategies to improve the performance of rotavirus vaccines in low SES. The immunogenicity of vaccines is likely to be the most directly modifiable of the factors investigated. Some vaccines in development, such as the neonatal 116E strain currently being trialed in India, may be more immunogenic than currently licensed vaccines. 
A second strategy to improve immunogenicity may be directed at the host. Delaying administration of vaccine from the current 6 and 10 weeks schedule (with RV1) to 10 and 14 weeks 
may also be an effective strategy to improve immunogenicity by allowing maternal antibody to wane for another four weeks 
, though this approach would have to be weighed against the risks of early natural infections and the potential risk of intussusception with later vaccination. A schedule with 3 doses of RV1 given at 6, 10, and 14 weeks might offer the most practical and programmatically feasible option, given that regulatory and economic considerations are satisfactorily addressed. We estimate that a third dose of vaccine may improve VE by approximately 9% in low SES. This finding is based on the assumption that a third dose of vaccine is as immunogenic as the first two doses, though there are little empirical data presently available to support this. 
Studies are needed to characterize the immune response and protection conferred by a third dose of vaccine, and to specifically determine if immunogenicity is compromised for doses administered at very young ages as a result of interference from maternal antibody.
In summary, this study demonstrates that even in their current sub-optimal state, rotavirus vaccines have the potential to substantially reduce severe diarrheal disease in very young children in low SES. By identifying and quantifying factors resulting in poorer vaccine performance in these settings, we are able to propose both a mechanism by which vaccination provides protection and an estimate of what can realistically be achieved. Modifying aspects of the vaccine (e.g. improving immunogenicity in low SES populations) or vaccination program (e.g. additional doses) may bring improvements, but in order to fully realize the benefits of the vaccine, interventions targeted at the host and the broader epidemiology of disease may be required.