Since 2006, two prophylactic human papillomavirus (HPV) vaccines have been widely used worldwide: the bivalent and quadrivalent vaccines. Both vaccines target HPV 16 and 18, which cause about 50% of high-grade cervical lesions, 70% of cervical cancers, and 40–80% of other HPV-related cancers.^1–5 The quadrivalent vaccine also targets HPV 6 and 11, which are associated with 80–90% of anogenital wart cases.⁶ Large randomised controlled clinical trials have shown that both vaccines are highly effective in protecting against vaccine-type persistent HPV infection and precancerous lesions in women and men (vaccine efficacy 93–100%).^7,8 More than 65 countries have introduced HPV vaccination programmes.^9,10 Most programmes target girls only, with only a handful of countries vaccinating both girls and boys (eg, the USA, Australia, Switzerland, Austria, and Canada).^11–17 These decisions have been made with substantial input from mathematical models.^11,18–22 Recently, a nonavalent vaccine, which targets HPV 31, 33, 45, 52, and 58 also, has been licensed and recommended for use in the USA²³ after reports of strong efficacy and immunogenicity from large trials.²⁴

Mathematical models have consistently predicted that vaccinating girls against HPV is highly cost-effective,^25–27 however, the picture is less clear for vaccinating boys.^28–35 This is because the cost-effectiveness of vaccinating girls is mainly driven by the direct benefit of HPV vaccination among vaccinated women, which depends on well quantified parameters such as vaccine efficacy and the proportion of cervical cancer due to the vaccine types.²⁷ The incremental effectiveness and cost-effectiveness of vaccinating boys is influenced largely by the magnitude of indirect protection conferred to men by vaccinating girls (herd immunity), which depends on a complex combination of factors (eg, vaccination coverage and sexual behaviour).^28,35,36 Modelling studies have shown that if vaccinating girls significantly reduces the burden of HPV-related diseases in men through herd immunity, then vaccinating boys will produce limited additional population-level benefits for heterosexual men and women and thus will not be cost-effective at the same vaccine price.^28,30,35 However, it is unclear what vaccination coverage is necessary to achieve substantial herd effects, and whether models are consistent in their predictions.

A systematic review of population-level HPV post-vaccination surveillance data has shown significant reductions in anogenital warts in young men in the first 4 years after girls-only quadrivalent vaccination programmes with high coverage (≥50%).³⁷ In countries with low vaccination coverage (<50%) there was no indication of herd effects.³⁷ In Australia, where quadrivalent vaccination coverage among girls has been consistently higher than 70%, anogenital warts consultations among heterosexual men declined by more than 80% within the first 5 years of the programme (before vaccination of boys).³⁸ These results suggest that HPV vaccination can produce important herd effects for the anogenital warts associated types (HPV 6 and 11), and that elimination of these types might be achievable.

Better understanding the potential long-term population-level effectiveness of HPV vaccination, including herd effects, is crucial to help inform future vaccine policy decisions such as the inclusion of boys in vaccination programmes, incremental impact of increasing vaccination coverage and optimal combinations of HPV vaccination and cervical cancer screening strategies. Mathematical models provide a formal framework to examine these questions, which cannot be answered in trial settings. However, models require many assumptions, which might lead to questions about the validity of predictions and uncertainty for decision makers. A large number of HPV models have been developed over the past decade, but it is still unclear whether the models are giving consistent results and whether we can draw general principles from them. We conducted a systematic review and meta-analysis of model predictions of the long-term population-level effectiveness of HPV vaccination against HPV 6, 11, 16, and 18 infection in women and men, to examine the robustness and variability of predicted herd effects, incremental benefit of vaccinating boys, and potential for HPV vaccine-type elimination.

Our search led to the identification of 51 articles published by 19 different research teams (figure 1). Of the 19 teams contacted to participate in the meta-analysis, 17 provided new standardised model predictions. All models met the main methodological quality criteria. However, one model⁴¹ was excluded because it was built for short-term predictions, and demographic change assumptions produced unstable long-term predictions. The 16 models included in the meta-analysis vary in terms of type (deterministic or stochastic), structure (assumptions about sexual activity, partnership formation and dissolution, transmission, and natural immunity), and baseline HPV prevalence, and were developed in ten countries (Australia, Canada, Finland, Germany, Ireland, Italy, Netherlands, Norway, UK, and USA; appendix pp 4–5). HPV 16, 18, 6, and 11 were included in 16, 13, five, and three models, respectively.

Among women after 70 years of girls-only vaccination, the overall predicted prevalence of HPV 16 decreased by 53% (RR_prev 0·53 [80% UI 0·46–0·68]) assuming 40% coverage, and by 93% (RR_prev 0·93 [80% UI 0·90–1·00]) assuming 80% coverage (figure 2). At 40% coverage, the corresponding RR_prev for HPV 6, 11, and 18 were 7 to 28 percentage points greater than HPV 16, and at 80% coverage these types were eliminated (HPV 11) or close to elimination (HPV 18 and 6; figure 3A, appendix pp 6–13). Given that population-level effectiveness (RR_prev) was substantially greater than vaccination coverage for all HPV vaccine-targeted types, these results indicate that girls-only vaccination is expected to produce substantial herd effects for unvaccinated women even at low coverage, with greater herd immunity effects for HPV 18, 6, and 11 than for HPV 16 (figure 3A, appendix p 14).

Important herd effects were also predicted in men after girls-only vaccination for both low and high coverage scenarios (figures 2, 3). Among men, the overall prevalence of HPV 16 decreased by 36% after 70 years of girls-only vaccination assuming 40% coverage (RR_prev 0·36 [80% UI 0·28–0·61]), and by 83% assuming 80% coverage (0·83 [0·75–1·00]; figure 2). The RR_prev of HPV 18, 6, and 11 were again greater than that of HPV 16 (figure 3A, appendix p 14).

Post-vaccination reduction in HPV prevalence over time after girls-only vaccination was faster for women than men, for types HPV 6 and 11 compared with HPV 16 and 18, and at higher coverage than at lower coverage (appendix pp 15–16).

Vaccinating 40% of boys in addition to 40% of girls (girls and boys strategy) resulted in incremental reductions of HPV 16 prevalence of 18% among women (incremental RR_prev 0·18 [80% UI 0·13–0·32]) and 35% among men (0·35 [0·27–0·39]) after 70 years (figure 2C). Given the important herd effects following girls-only vaccination with 80% coverage, vaccinating 80% of boys in addition to girls produced small incremental reductions in HPV 16 prevalence (incremental RR_prev of 0·07 [80% 0·00–0·10] for women and 0·16 [80% 0·01–0·25] for men), after 70 years (figure 2D). The incremental population-level effectiveness of vaccinating boys in addition to girls was similar between the HPV vaccine types when assuming 40% coverage, but was substantially higher for HPV 16 (vs HPV 18, 6, 11) when assuming 80% coverage (figure 3B). Vaccinating boys in addition to girls produced a slightly faster decline in vaccine-type-specific prevalence among women and men (appendix pp 15–16).

For the same number of additional vaccinated individuals, increasing coverage in a girls-only strategy was predicted to provide greater population-level benefits than was including boys in a vaccination programme. The models predicted that increasing girls-only vaccination coverage by 40% (from 40% to 80%) reduced HPV 16, 18, 6, and 11 prevalence in women by an additional 40%, 38%, 35%, and 19%, respectively; higher than the incremental benefits of vaccinating 40% of boys in addition to 40% of girls (figure 4; appendix pp 10–13, 15–16). The same increase in girls-only vaccination coverage from 40% to 80% was also more effective in reducing HPV 16, 18, and 6 prevalence in men than the incremental benefit of vaccinating 40% of boys in addition to 40% of girls, and the strategies were equally effective for HPV 11 (figure 4, appendix pp 10–13).

Increasing coverage considerably improved population-level effectiveness up to 80% for girls-only vaccination and 60% for girls and boys vaccination, after which, increasing coverage had very little marginal benefit (figure 4). Substantial herd effects were predicted with girls-only vaccination coverage as low as 20% (figure 4, appendix pp 10–13). Interestingly, 19% (three of 16), 46% (six of 13), 60% (three of five), and 100% (three of three) of models predicted that HPV 16, 18, 6, and 11, respectively, would be eliminated among heterosexual populations if girls-only vaccination reaches 80% coverage (figure 4, appendix p 14). The girls and boys strategy substantially increased the predicted potential for elimination; 64%, 92%, 80%, and 100% of models predicted that HPV 16, 18, 6, and 11 would be eliminated with 80% coverage, and a few models predicted elimination of types HPV 18, 6, and 11 with 60% coverage (figure 4, appendix p 14).

Predicted population-level effectiveness and herd effects were much lower and more variable across the models when assuming that vaccine duration of protection was 20 years compared with lifelong protection (appendix p 17). However, reducing vaccine efficacy from 100% to 90% had little impact on the pooled predictions (appendix p 17).

In the meta-regression analysis, vaccination coverage and vaccination strategies were the main sources of heterogeneity between the predictions of the models (data not shown). However, the meta-regression results are presented separately by vaccination coverage and vaccination strategy, given that significant interactions were observed between these variables and the other model characteristics (appendix pp 18–19). Across all vaccination scenarios, the main source of heterogeneity in predictions for women and men was whether the transmission-dynamic models included (or not) different sexual activity risk groups (appendix pp 18–19). Models that did not include risk groups for sexual activity predicted significantly higher population-level HPV vaccination effectiveness and herd effects. Population-level effectiveness was also significantly higher among models that assume lower natural immunity among women (mostly when vaccine protection is assumed lifelong), or include the natural history of cervical cancer (when vaccine protection is 20 years). These results were similar when examining model predictions for HPV 18.

The findings from our systematic review and meta-analysis suggest that HPV vaccination will produce strong herd effects leading to substantial long-term reductions in HPV infection and related diseases in unimmunised women and men. Herd effects are predicted even with vaccination coverage as low as 20%, and to be greater for HPV 18, 6, and 11 types than for HPV 16. Given the substantial herd effects of girls-only vaccination when coverage is moderate to high, the incremental benefit of vaccinating boys is predicted to be small. However, most models predict that vaccinating boys in addition to girls could eliminate HPV 16, 18, 6, and 11, as long as 80% coverage is achieved in both sexes and the vaccine confers long-term protection.

Our findings have important policy implications. First, because of the important herd effects from girls-only vaccination, our models predict that increasing HPV vaccination coverage among girls has greater incremental benefit for both male and female individuals than adding boys to a vaccination programme. The herd effects for heterosexual men are predicted to be about the same magnitude as the level of girls-only vaccination coverage. Given this, the epidemiological and economic considerations about vaccinating boys should focus on the following issues: the feasibility and incremental marginal costs of increasing vaccination coverage among girls versus introducing a gender-neutral programme;⁴² whether the price of the vaccine can be reduced for boys for the strategy to be cost-effective; and the importance placed on achieving equal protection for men who have sex with men (MSM).

Second, our models suggest that elimination of HPV 6, 11, and 18 is likely if vaccination coverage of girls and boys reaches 80% and the vaccine provides long-term protection. However, vaccination coverage might have to be slightly higher than 80% to eliminate HPV 16, the type responsible for most of the HPV-related burden. These results also have implications for the recently licensed nonavalent vaccine. Given their prevalence and biological characteristics, the additional types are expected to behave similarly to type HPV 18 and thus be easier to eliminate than HPV 16. It should also be noted that the time to elimination might be shorter than was predicted in the meta-analysis (appendix pp 15–16), because we did not include scenarios with catch-up programmes. Policy makers might want to examine whether to set objectives to eliminate HPV vaccine types in their jurisdictions and set vaccination coverage targets.

Third, post-vaccination reduction of HPV 6 and 11 infections was predicted to be steeper than for HPV 16 and 18 infections, which is due to the shorter durations of infectiousness and lower transmissibility of these low oncogenic risk types.⁴³ Hence, HPV 6 and 11-related disease (eg, anogenital warts) trends are a poor proxy of change in HPV 16 and 18 and related diseases, and should not be directly extrapolated to inform policy decisions regarding prevention of HPV-related cancers and its precursors.

Fourth, the models predicted substantial herd effects even at relatively lower coverage (40%). However, a recent meta-analysis found evidence of significant herd effects only in higher-coverage settings.³⁷ Our study findings suggest this difference is likely to be because herd effects take longer to become evident where coverage is lower. Early programme impact data should not be used to rule out herd effects in settings where coverage is low.

This study addresses a key source of concern when using mathematical model results for decision making: the robustness and validity of predictions. By systematically identifying published HPV transmission-dynamic models that were independently developed from one another and presenting the distribution of predictions, our analysis provides decision makers with a measure of uncertainty and robustness surrounding model predictions. Reassuringly, the key conclusions of this systematic review were consistent among the models, even though the models were built to represent different countries and varied in structure and assumptions.

According to good modelling practice guidelines, model validation should include between-model corroboration using independent models and, if possible, external or predictive validation.⁴⁴ Our systematic review shows high consistency in HPV model predictions of population-level reductions in HPV vaccine types among women and men when vaccination coverage is 80% or higher for girls only and 60% or higher for girls and boys vaccination. The models also consistently predict that post-vaccination reductions will be smaller for HPV 16 than the other vaccine types. However, there is substantial variability in predictions when vaccination coverage is between 40–60%, and when duration of vaccine protection is 20 years. Our meta-regression identified two key model choices or parameters that explain this variability: inclusion of sexual activity risk groups in the model and the level of natural immunity among women. Sexual activity has been shown to be very heterogeneous in populations (eg, skewed distribution of number of partners), leading most models built for prediction of interventions against sexually transmitted diseases to include sexual risk groups. Furthermore, a recent meta-analysis found that the proportion of women who develop natural immunity against a subsequent HPV 16 or 18 infection is greater than 35% when controlling for potential confounders or using neutralising assays.⁴⁵ When considering only the predictions of models that include different sexual activity risk groups and that assume that the proportion of women who develop natural immunity is greater than 35%, the variability in predictions is substantially reduced with little impact on the median pooled estimates (eg, at 40% vaccination coverage, the RR_prev of HPV 16 among women after girls-only vaccination is 0·52 [80% UI 0·45–0·58] vs 0·53 [0·46–0·68] when considering all predictions (appendix pp 20–21). Finally, although external or predictive validation was beyond the scope of the paper, the descriptive results of the pooled analysis are in line with results from a recent meta-analysis of post-HPV vaccination data,³⁷ showing strong herd effects shortly after vaccination in countries with high vaccination coverage and very little evidence of herd effects in this timeframe where coverage is low. In addition, models included in the systematic review have previously shown that they reproduce the reduction in HPV 16 and 18 infection^46,47 and anogenital warts consultations observed in the first 5 years after HPV vaccination introduction.⁴⁸

Our main findings are likely generalisable to most high-income countries given that they are based on models from ten of these countries and very little heterogeneity remains when results are stratified by vaccination coverage, vaccination strategy, and key model characteristics. In addition, there are similarities in sexual behaviour,⁴⁹ HPV type distribution,^50,51 and age profile of HPV prevalence⁵² among high-income countries. However, our predicted herd effects and potential for elimination should be extrapolated to low-income and middle-income countries (LMIC) with caution, because there are important differences between high-income countries and LMICs in sexual behaviour and potential cofactors of HPV such as high HIV prevalence.^49,53,54

The study has two main limitations that should be considered, in addition to those inherent in meta-analysis.^55,56 First, although the models were built independently from one another and showed variability in their structures, similarities remain in key structural assumptions, which could contribute to the consistency of findings. None of the models included MSM, incorporated multisite infection or transmission (transmission between oral, anal, and genital sites), or the possibility of reactivation. Modelling HPV transmission between men would be unlikely to have an effect on predictions about the herd effects of girls-only vaccination, but could slightly impact predictions about elimination. Including higher risk groups or MSM, who have greater HPV prevalence (and higher R₀), would make it more difficult to eliminate HPV, and therefore the coverage required for elimination could be higher than estimated by the models in the systematic review. On the other hand, recent modelling studies suggest that adding multisite transmission or reactivation would probably have very little impact on long-term predictions about the population-level effectiveness of HPV vaccination.^57,58 Second, we purposely decided to examine the predicted impact of vaccination on HPV infection rather than disease endpoints, as the main focus of the paper is on herd effects and elimination of HPV vaccine types. Additional uncertainty in HPV model predictions, when examining the impact of vaccination on disease endpoints, will be in the absolute reduction of HPV burden of disease (related to country specific pre-vaccination burden of disease and proportion due to the vaccine types) and the timing of these benefits (related to assumptions about progression from infection to lesions or cancer).

To our knowledge, our study includes a greater number of models than any published comparison of infectious disease models, reflecting the influential role that modelling has played in HPV vaccination policy decisions. Furthermore, this is the first model comparison study in which systematic review methodology was used to identify all potentially eligible mathematical models (reducing possible selection bias); independence of models was controlled for by including only one model per team and producing predictions for predetermined and standardised scenarios without prior harmonisation of model structures or natural history parameters; and meta-analytic techniques were used to describe the central tendency and variability of predictions and identify sources of heterogeneity in results. Finally, our study shows that the HPV models developed over the past decade give consistent results in terms of population-level effectiveness against infection, herd effects, and the possibility of elimination, which could be reassuring for decision makers using these models for vaccination policy decisions. We also identified key HPV modelling choices (ie, inclusion of sexual risk groups, natural history of cervical cancer, and natural immunity) that have the greatest influence on model predictions, which should guide the future development of models.

In conclusion, the results of this study indicate strong promise for the long-term population-level impact of HPV vaccination programmes. However, it will be important to continue to validate HPV model predictions and to compare them to post-vaccination surveillance data, as many policy decisions about HPV vaccination (ie, number of doses, which vaccine to use, and vaccination of boys) and cervical cancer screening remain.