Vaccination against multiple HPV types

Effective vaccination strategies for human papillomavirus (HPV) infection and cervical cancer based on the mathematical model with a stochastic process

Human papillomavirus (HPV) infection poses a significant risk to women's health by causing cervical cancer. In addition to HPV, cervical cancer incidence rates can be influenced by various factors, including human immunodeficiency virus and herpes, as well as screening policy. In this study, a mathematical model with stochastic processes was developed to analyze HPV transmission between genders and its subsequent impact on cervical cancer incidence. The model simulations suggest that both-gender vaccination is far more effective than female-only vaccination in preventing an increase in cervical cancer incidence. With increasing stochasticity, the difference between the number of patients in the vaccinated group and the number in the nonvaccinated group diminishes. To distinguish the patient population distribution of the vaccinated from the nonvaccinated, we calculated effect size (Cohen's distance) in addition to Student's t-test. The model analysis suggests a threshold vaccination rate for both genders for a clear reduction of cancer incidence when significant stochastic factors are present.

Biological, demographic, and health factors associated with HPV infection in Ecuadorian women

Objectives

The study aims to identify the correlation between human papillomavirus (HPV) infection and sociodemographic and sexual reproductive health factors in Ecuadorian women from March to August 2019.

Methods

120 women were randomly selected from two gynecological clinics to complete a questionnaire and provide a biospecimen. PCR-Hybridization was used to genotype 37 HPV serotypes in samples obtained by endo-cervical brushing for liquid-based cytology. Sociodemographic and sexual health data were collected through a validated questionnaire during a medical consultation. Mathematical modeling of HPV infection was done using bivariate logistic regression.

Results

65.0% of the women sampled had an HPV infection; 74.3% of these women had co-infections with other HPV genotypes. Out of the women who were HPV positive, 75.6% were diagnosed with high-risk genotypes from HPV strains 18, 35, 52, and 66. Parity, immunosuppression, and use of oral contraception/intrauterine devices (IUDs) were identified as associated variables. The explanatory model had a sensitivity of 89.5% and a specificity of 73.8%.

Conclusion

The predominant strains of HPV among Ecuadorian women are diverse. The risk of HPV infection is a complex phenomenon where biological and psychosocial variables are integrated into a model. In populations with limited access to health services, low socioeconomic status, and negative sociocultural beliefs about sexually transmitted infections (STIs), surveys can be used as a pre-screening step for HPV infections. The diagnostic value of the model should be tested in multicenter studies that include women from all over the country.

High Prevalence of HPV 51 in an Unvaccinated Population and Implications for HPV Vaccines

Human papillomavirus (HPV) is detected in 99.7% of cervical cancers. Current vaccines target types 16 and 18. Prior to vaccination implementation, a prospective cohort study was conducted to determine baseline HPV prevalence in unvaccinated women in Wales; after HPV16 and HPV18, HPV 51 was found to be most prevalent. This study aimed to re-assess the unexpected high prevalence of HPV 51 and consider its potential for type-replacement. Two hundred HPV 51 positive samples underwent re-analysis by repeating the original methodology using HPV 51 GP5+/6+ PCR-enzyme immunoassay, and additionally a novel assay of HPV 51 E7 PCR. Data were correlated with age, social deprivation and cytology. Direct repeat of HPV 51 PCR-EIA identified 146/195 (75.0%) samples as HPV 51 positive; E7 PCR identified 166/195 (85.1%) samples as HPV 51 positive. HPV 51 prevalence increased with cytological grade. The prevalence of HPV 51 in the pre-vaccinated population was truly high. E7 DNA assays may offer increased specificity for HPV genotyping. Cross-protection of current vaccines against less-prevalent HPV types warrants further study. This study highlights the need for longitudinal investigation into the prevalence of non-vaccine HPV types, especially those phylogenetically different to vaccine types for potential type-replacement. Ongoing surveillance will inform future vaccines.

Assessing the best time interval between doses in a two-dose vaccination regimen to reduce the number of deaths in an ongoing epidemic of SARS-CoV-2

The SARS-CoV-2 pandemic is a major concern all over the world and, as vaccines became available at the end of 2020, optimal vaccination strategies were subjected to intense investigation. Considering their critical role in reducing disease burden, the increasing demand outpacing production, and that most currently approved vaccines follow a two-dose regimen, the cost-effectiveness of delaying the second dose to increment the coverage of the population receiving the first dose is often debated. Finding the best solution is complex due to the trade-off between vaccinating more people with lower level of protection and guaranteeing higher protection to a fewer number of individuals. Here we present a novel extended age-structured SEIR mathematical model that includes a two-dose vaccination schedule with a between-doses delay modelled through delay differential equations and linear optimization of vaccination rates. By maintaining the minimum stock of vaccines under a given production rate, we evaluate the dose interval that minimizes the number of deaths. We found that the best strategy depends on an interplay between the vaccine production rate and the relative efficacy of the first dose. In the scenario of low first-dose efficacy, it is always better to vaccinate the second dose as soon as possible, while for high first-dose efficacy, the best strategy of time window depends on the production rate and also on second-dose efficacy provided by each type of vaccine. We also found that the rate of spread of the infection does not affect significantly the thresholds of the best window, but is an important factor in the absolute number of total deaths. These conclusions point to the need to carefully take into account both vaccine characteristics and roll-out speed to optimize the outcome of vaccination strategies.

Mathematical assessment of the impact of cohort vaccination on pneumococcal carriage and serotype replacement

Although pneumococcal vaccines are quite effective in reducing disease burden, factors such as imperfect vaccine efficacy and serotype replacement present an important challenge against realizing direct and herd protection benefits of the vaccines. In this study, a novel mathematical model is designed and used to describe the dynamics of two Streptococcus pneumoniae (SP) serotypes, in response to the introduction of a cohort vaccination program which targets one of the two serotypes. The model is fitted to a pediatric SP carriage prevalence data from Atlanta, GA. The model, which is rigorously analysed to investigate the existence and asymptotic stability properties of the associated equilibria (in addition to exploring conditions for competitive exclusion), is simulated to assess the impact of vaccination under different levels of serotype-specific competition and illustrate the phenomenon of serotype replacement. The calibrated model is used to forecast the carriage prevalence in the pediatric cohort over 30 years.

Two-sex logistic model for human papillomavirus and optimal vaccine

We formulate a two-gender susceptible–infectious–susceptible (SIS) model to search for optimal childhood and catch-up vaccines over a 20-year period. The optimal vaccines should minimize the cost of Human Papillomavirus (HPV) disease in random logistically growing population. We find the basic reproduction number [Formula: see text] for the model and use it to describe the local-asymptotic stability of the disease-free equilibrium (DFE). We estimate the solution of the model to show the role of vaccine in reducing [Formula: see text] and controlling the disease. We formulate some optimal control problems to find the optimal vaccines needed to control HPV under limited resources. The optimal vaccines needed to keep [Formula: see text] are the catch-up vaccine rates of 0.004 and 0.005 for females and males, respectively; 100[Formula: see text] is needed to reduce [Formula: see text] to its minimum value. To reduce the expenses for HPV disease and its vaccines, we need 100[Formula: see text] childhood vaccines (both genders) for the first 13–14 years and then gradually reduce the vaccine to reach [Formula: see text] at year 20. For adults (both genders), we need maximum rates (one) for the first 9 years, then [Formula: see text] for the next 3–4 years before reducing gradually to zero rate at year 20. Although the childhood vaccines provide very early protection strategy against HPV, its time to control HPV is longer than that for adult vaccines. Thus, full adults’ only vaccines for enough period is a viable choice to control HPV at minimal cost and short time.

A Dynamic Model to Assess Human Papillomavirus Vaccination Strategies in a Heterosexual Population Combined with Men Who have Sex with Men

Vaccination is effective in preventing human papillomavirus (HPV) infection. It is imperative to investigate who should be vaccinated and what the best vaccine distribution strategy is. In this paper, we use a dynamic model to assess HPV vaccination strategies in a heterosexual population combined with gay, bisexual, and other men who have sex with men (MSM). The basic reproduction numbers for heterosexual females, heterosexual males and MSM as well as their average for the total population are obtained. We also derive a threshold parameter, based on basic reproduction numbers, for model analysis. From the analysis and numerical investigations, we have several conclusions. (1) To eliminate HPV infection, the priority of vaccination should be given to MSM, especially in countries that have already achieved high coverage in females. The heterosexual population gets great benefit but MSM only get minor benefit from vaccinating heterosexual females or males. (2) The best vaccination strategy is to vaccinate MSM firstly as many as possible, then heterosexual females, lastly heterosexual males. (3) Given a fixed vaccination coverage of MSM, distributing the remaining vaccines to only heterosexual females or males leads to a similar prevalence in the total population. This prevalence is lower than that when vaccines are distributed to both genders. The evener the distribution, the higher the prevalence in the total population. (4) Vaccination becomes less effective in reducing the prevalence as more vaccines are given. It is more effective to allocate vaccines to a region with lower vaccination coverage. This study provides information that may help policymakers formulate guidelines for vaccine distribution to reduce HPV prevalence on the basis of vaccine availability and prior vaccination coverage. Whether these guidelines are affected when the objective is to reduce HPV-associated cancer incidence remains to be further studied.

Untangling the dynamics of persistence and colonization in microbial communities

A central goal of community ecology is to infer biotic interactions from observed distributions of co-occurring species. Evidence for biotic interactions, however, can be obscured by shared environmental requirements, posing a challenge for statistical inference. Here, we introduce a dynamic statistical model, based on probit regression, that quantifies the effects of spatial and temporal covariance in longitudinal co-occurrence data. We separate the fixed pairwise effects of species occurrences on persistence and colonization rates, a potential signal of direct interactions, from latent pairwise correlations in occurrence, a potential signal of shared environmental responses. We first validate our modeling framework with several simulation studies. Then, we apply the approach to a pressing epidemiological question by examining how human papillomavirus (HPV) types coexist. Our results suggest that while HPV types respond similarly to common host traits, direct interactions are sparse and weak, so that HPV type diversity depends largely on shared environmental drivers. Our modeling approach is widely applicable to microbial communities and provides valuable insights that should lead to more directed hypothesis testing and mechanistic modeling.

Models to predict the public health impact of vaccine resistance: A systematic review

Pathogen evolution is a potential threat to the long-term benefits provided by public health vaccination campaigns. Mathematical modeling can be a powerful tool to examine the forces responsible for the development of vaccine resistance and to predict its public health implications. We conducted a systematic review of existing literature to understand the construction and application of vaccine resistance models. We identified 26 studies that modeled the public health impact of vaccine resistance for 12 different pathogens. Most models predicted that vaccines would reduce overall disease burden in spite of evolution of vaccine resistance. Relatively few pathogens and populations for which vaccine resistance may be problematic were covered in the reviewed studies, with low- and middle-income countries particularly under-represented. We discuss the key components of model design, as well as patterns of model predictions.

Inferring Pathogen Type Interactions Using Cross-sectional Prevalence Data: Opportunities and Pitfalls for Predicting Type Replacement

BACKGROUND

Many multivalent vaccines target only a subset of all pathogenic types. If vaccine and nonvaccine types compete, vaccination may lead to type replacement. The plausibility of type replacement has been assessed using the odds ratio (OR) of co-infections in cross-sectional prevalence data, with OR > 1 being interpreted as low risk of type replacement. The usefulness of the OR as a predictor for type replacement is debated, as it lacks a theoretical justification, and there is no framework explaining under which assumptions the OR predicts type replacement.

METHODS

We investigate the values that the OR can take based on deterministic S usceptible- I infected- S usceptible and S usceptible- Infected- Recovered- S usceptible multitype transmission models. We consider different mechanisms of type interactions and explore parameter values ranging from synergistic to competitive interactions.

RESULTS

We find that OR > 1 might mask competition because of confounding due to unobserved common risk factors and cross-immunity, as indicated by earlier studies. We prove mathematically that unobserved common risk factors lead to an elevation of the OR, and present an intuitive explanation why cross-immunity increases the OR. We find that OR < 1 is predictive for type replacement in the absence of immunity. With immunity, OR < 1 remains predictive under biologically reasonable assumptions of unidirectional interactions during infection, and an absence of immunity-induced synergism.

CONCLUSIONS

Using the OR in cross-sectional data to predict type replacement is justified, but is only unambiguous under strict assumptions. An accurate prediction of type replacement requires pathogen-specific knowledge on common risk factors and cross-immunity.

Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model reveal that with 70% condom compliance by the male population, administering female vaccine (with 45% efficacy) is sufficient for effective control of the disease.

Random Network Models to Predict the Long-Term Impact of HPV Vaccination on Genital Warts

The Human papillomaviruses (HPV) vaccine induces a herd immunity effect in genital warts when a large number of the population is vaccinated. This aspect should be taken into account when devising new vaccine strategies, like vaccination at older ages or male vaccination. Therefore, it is important to develop mathematical models with good predictive capacities. We devised a sexual contact network that was calibrated to simulate the Spanish epidemiology of different HPV genotypes. Through this model, we simulated the scenario that occurred in Australia in 2007, where 12-13 year-old girls were vaccinated with a three-dose schedule of a vaccine containing genotypes 6 and 11, which protect against genital warts, and also a catch-up program in women up to 26 years of age. Vaccine coverage were 73 % in girls with three doses and with coverage rates decreasing with age until 52 % for 20-26 year-olds. A fast 59 % reduction in the genital warts diagnoses occurred in the model in the first years after the start of the program, similar to what was described in the literature.

An age-structured model of the human papillomavirus dynamics and optimal vaccine control

We formulate an age-structured model based on a system of nonlinear partial differential equations to assist the early and catch up female vaccination programs for human papillomavirus (HPV) types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible (SIS) structure. We calculate the effective reproduction number [Formula: see text] for the model and describe the local-asymptotic stability of the disease-free equilibrium using [Formula: see text]. We prove the existence of an endemic equilibrium for [Formula: see text] for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.

Bias Due to Correlation Between Times-at-Risk for Infection in Epidemiologic Studies Measuring Biological Interactions Between Sexually Transmitted Infections: A Case Study Using Human Papillomavirus Type Interactions

The clustering of human papillomavirus (HPV) infections in some individuals is often interpreted as the result of common risk factors rather than biological interactions between different types of HPV. The intraindividual correlation between times-at-risk for all HPV infections is not generally considered in the analysis of epidemiologic studies. We used a deterministic transmission model to simulate cross-sectional and prospective epidemiologic studies measuring associations between 2 HPV types. When we assumed no interactions, the model predicted that studies would estimate odds ratios and incidence rate ratios greater than 1 between HPV types even after complete adjustment for sexual behavior. We demonstrated that this residual association is due to correlation between the times-at-risk for different HPV types, where individuals become concurrently at risk for all of their partners' HPV types when they enter a partnership and are not at risk when they are single. This correlation can be controlled in prospective studies by restricting analyses to susceptible individuals with an infected sexual partner. The bias in the measured associations was largest in low-sexual-activity populations, cross-sectional studies, and studies which evaluated infection with a first HPV type as the exposure. These results suggest that current epidemiologic evidence does not preclude the existence of competitive biological interactions between HPV types.

The optimal treatment of an infectious disease with two strains

This paper explores the optimal treatment of an infectious disease in a Susceptible-Infected-Susceptible model, where there are two strains of the disease and one strain is more infectious than the other. The strains are perfectly distinguishable, instantly diagnosed and equally costly in terms of social welfare. Treatment is equally costly and effective for both strains. Eradication is not possible, and there is no superinfection. In this model, we characterise two types of fixed points: coexistence equilibria, where both strains prevail, and boundary equilibria, where one strain is asymptotically eradicated and the other prevails at a positive level. We derive regimes of feasibility that determine which equilibria are feasible for which parameter combinations. Numerically, we show that optimal policy exhibits switch points over time, and that the paths to coexistence equilibria exhibit spirals, suggesting that coexistence equilibria are never the end points of optimal paths.

Primary strategies for HPV infection and cervical cancer prevention

Counseling messages for tobacco cessation, condom use, circumcision, and selective choice in the number of sexual partners can help reduce the risk of cervical cancer. Other sexual behavioral and reproductive risk factors for cervical cancer are a younger age at first intercourse and at first full-term pregnancy as well as increasing duration of combined hormonal oral contraceptive use. Micronutrients and supplements can reduce the risk of human papillomavirus infection, persistence, progression, and regression. Some human papillomavirus infections can be prevented by vaccination. Cervical cancer is best prevented by screening.

DYNAMICS ANALYSIS OF A VACCINATION MODEL FOR HPV TRANSMISSION

A new deterministic model for the transmission dynamics of human papillomavirus (HPV) and related cancers, in the presence of the Gardasil vaccine (which targets four HPV types), is presented. In the absence of routine vaccination in the community, the model is shown to undergo the phenomenon of backward bifurcation. This phenomenon, which has important consequences on the feasibility of effective disease control in the community, arises due to the re-infection of recovered individuals. For the special case when backward bifurcation does not occur, the disease-free equilibrium (DFE) of the model is shown to be globally-asymptotically stable (GAS) if the associated reproduction number is less than unity. The model with vaccination is also rigorously analyzed. Numerical simulations of the model with vaccination show that, with the assumed 90% efficacy of the Gardasil vaccine, the effective community-wide control of the four Gardasil-preventable HPV types is feasible if the Gardasil coverage rate is high enough (in the range 78–88%).

Population- and type-specific clustering of multiple HPV types across diverse risk populations in the Netherlands

In view of possible type replacement upon introduction of human papillomavirus (HPV) vaccination, we aimed to explore patterns of type-specific clustering across populations with various background infection risks. A total of 3,874 women from 3 cross-sectional studies in the Netherlands (in 2007-2009) provided vaginal self-samples, which were tested for 25 HPV genotypes by a sensitive molecular assay (SPF10 line probe assay, DDL Diagnostic Laboratory, Voorburg, the Netherlands). The number of concurrent HPV infections per woman was studied by Poisson regression. Associations between HPV types were investigated by generalized estimating equation analyses. The prevalence of any HPV type was 14% in a population-based study, 54% in a chlamydia screening intervention study, and 73% in a study among attendees of sexually transmitted infection clinics. Overall, multiple HPV infections were detected in 26% of the women. The number of concurrent HPV infections conformed to an overdispersed Poisson distribution, even after correction for known risk factors. Types differed significantly in their tendencies to be involved in coinfections, but no evidence for particular type-type interactions was found. Moreover, the strongest associations were observed in the lowest-risk population and vice versa.We found no indications of pairwise interactions, but our findings do suggest that clustering differs among HPV types and varies across risk groups.

Revising ecological assumptions about Human papillomavirus interactions and type replacement

The controversy over whether vaccine-targeted HPV types will be replaced by other oncogenic, non-vaccine-targeted types remains unresolved. This is in part because little is known about the ecology of HPV types. Patient data has been interpreted to suggest independence or facilitative interactions between types and therefore replacement is believed to be unlikely. With a novel mathematical model, we investigated which HPV type interactions and their immune responses gave qualitatively similar patterns frequently observed in patients. To assess the possibility of type replacement, vaccination was added to see if non-vaccine-targeted types increased their 'niche'. Our model predicts that independence and facilitation are not necessary for the coexistence of types inside hosts, especially given the patchy nature of HPV infection. In fact, independence and facilitation inadequately represented co-infected patients. We found that some form of competition is likely in natural co-infections. Hence, non-vaccine-targeted types that are not cross-reactive with the vaccine could spread to more patches and can increase their viral load in vaccinated hosts. The degree to which this happens will depend on replication and patch colonization rates. Our results suggest that independence between types could be a fallacy, and so without conclusively untangling HPV within-host ecology, type replacement remains theoretically viable. More ecological thinking is needed in future studies.

Randomization modeling to ascertain clustering patterns of human papillomavirus types detected in cervicovaginal samples in the United States

Detection of multiple human papillomavirus (HPV) types in the genital tract is common. Associations among HPV types may impact HPV vaccination modeling and type replacement. The objectives were to determine the distribution of concurrent HPV type infections in cervicovaginal samples and examine type-specific associations. We analyzed HPV genotyping results from 32,245 cervicovaginal specimens collected from women aged 11 to 83 years in the United States from 2001 through 2011. Statistical power was enhanced by combining 6 separate studies. Expected concurrent infection frequencies from a series of permutation models, each with increasing fidelity to the real data, were compared with the observed data. Statistics were computed based on the distributional properties of the randomized data. Concurrent detection occurred more than expected with 0 or ≥3 HPV types and less than expected with 1 and 2 types. Some women bear a disproportionate burden of the HPV type prevalence. Type associations were observed that exceeded multiple hypothesis corrected significance. Multiple HPV types were detected more frequently than expected by chance and associations among particular HPV types were detected. However vaccine-targeted types were not specifically affected, supporting the expectation that current bivalent/quadrivalent HPV vaccination will not result in type replacement with other high-risk types.

A NOVEL APPLICATION OF A CLASSICAL METHOD FOR CALCULATING THE BASIC REPRODUCTIVE NUMBER, R0 FOR A GENDER AND RISK STRUCTURED TRANSMISSION DYNAMIC MODEL OF HUMAN PAPILLOMAVIRUS INFECTION

Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human Papillomavirus (HPV). Here, an ordinary differential equation (ODE) transmission dynamic model for HPV is presented and analyzed. Parameter values for a gender and risk structured model are estimated by calibrating the model around the known prevalence of infection. The effect on gender and risk sub-group prevalence induced by varying the epidemiological parameters are investigated. Finally, the outcomes of this model are applied using a classical mathematical method for calculating R0 in a heterogeneous mixing population. Estimates for R0 under various gender and mixing scenarios are presented.

The Cost-Effectiveness Analysis of a Quadrivalent Human Papillomavirus Vaccine (6/11/16/18) for Females in Japan

OBJECTIVE

We assessed the epidemiological and economic impact of a quadrivalent human papillomavirus (HPV) (6/11/16/18) vaccine for females in preventing cervical cancer, cervical intraepithelial neoplasia grades 2 and 3 (CIN 2/3), cervical intraepithelial neoplasia grade 1 (CIN 1), and genital warts in Japan by using a transmission dynamic model.

METHODS

A published mathematical model of the transmission dynamics of HPV infection and disease was adapted for Japan. Model inputs were used from Japan or the Asia/Pacific region when available; otherwise, the default values in the original model were used. The transmission dynamic model was used to assess the epidemiological and economic impact of a quadrivalent HPV (6/11/16/18) vaccine for females in preventing cervical cancer, CIN 2/3, CIN 1, and genital warts in Japan.Maintaining current cervical cancer screening practices, we evaluated two strategies: routine vaccination of females by age 12 years (S1), and S1 combined with a temporary (5 years) female catch-up program for age 12 to 24 years (S2). The vaccine coverage rate was 80% for the routine and 50% for the catch-up vaccination programs.

RESULTS

Compared with no vaccination, both vaccination strategies significantly reduced the incidence of HPV 6/11/16/18-related disease. The most effective strategy was S2. By using this strategy over 100 years in the Japanese population, the estimated cumulative percentage reduction in incident HPV 6/11/16/18-related genital warts-female, genital warts-male, cervical CIN 1, CIN 2/3, and cervical cancer cases was 90% (2,113,723 cases), 86% (2,082,637 cases), 72% (263,406 cases), 71% (1,328,366 cases), and 58% (323,145 cases), respectively. The cost-effectiveness ratios were JPY 1,244,000, and JPY 1,205,800 per quality-adjusted life-year gained for S1 and S2 compared with no vaccination, respectively, over a time horizon of 100 years.

CONCLUSION

We conclude that a quadrivalent HPV vaccination program for females can reduce the incidence of cervical cancer, CIN, and genital warts in Japan at a cost-per-quality-adjusted life-year ratio within the range defined as cost-effective.

Estimating the long-term effects of HPV vaccination in Germany

In Germany, vaccination against the most oncogenic HPV types 16/18 is recommended by the Standing Committee on Vaccination (STIKO) for 12-17 year old girls since March 2007. We developed a dynamic mathematical model for the natural history and transmission of HPV infections to estimate the impact of vaccination on incidence and mortality of cervical cancer and its pre-stages, and on anogenital warts. We focused on an extensive model calibration to epidemiologic data for all stages of the natural history model as well as on a detailed implementation of cervical cancer screening modalities in Germany. Our model predicts first a substantial reduction of cervical cancer incidence and mortality over the next 30 years, which is mainly attributable to an increase in screening participation in the 1990s and not to HPV vaccination, followed by a further reduction attributable to vaccination. Over the next 100 years, HPV vaccination will prevent approximately 37% of cervical cancer cases even if vaccination coverage is only 50% (as currently observed in Germany). Consideration of cross-protection results in a further reduction of approximately 7% of all cervical cancer cases for the bivalent and about 5% for the quadrivalent vaccine in our model. Vaccination of boys was only reasonable if moderate to high vaccination coverage in girls was not achieved. Strategies should be implemented in Germany to increase HPV vaccination coverage among girls thereby making better use of the demonstrated benefits of the vaccine.

Aggregation and competitive exclusion: explaining the coexistence of human Papillomavirus types and the effectiveness of limited vaccine conferred cross-immunity

Human Papillomavirus (HPV) types are sexually transmitted infections that cause a number of human cancers. According to the competitive exclusion principle in ecology, HPV types that have lower transmission probabilities and shorter durations of infection should be outcompeted by more virulent types. This, however, is not the case, as numerous HPV types co-exist, some which are less transmissible and more easily cleared than others. This paper examines whether this exception to the competitive exclusion principle can be explained by the aggregation of infection with HPV types, which results in patchy spatial distributions of infection, and what implications this has for the effect of vaccination on multiple HPV types. A deterministic transmission model is presented that models the patchy distribution of infected individuals using Lloyd's mean crowding. It is first shown that higher aggregation can result in a reduced capacity for onward transmission and reduce the required efficacy of vaccination. It is shown that greater patchiness in the distribution of lower prevalence HPV types permits co-existence. This affirms the hypothesis that the aggregation of HPV types provides an explanation for the violation of the competitive exclusion principle. Greater aggregation of lower prevalence types has important implications where type-specific HPV vaccines also offer cross-protection against non-target types. It is demonstrated that the degree of cross-protection can be less than the degree of vaccine protection conferred against directly targeted types and still result in the elimination of non-target types when these non-target types are patchily distributed.

Reevaluation of epidemiological data demonstrates that it is consistent with cross-immunity among human papillomavirus types

BACKGROUND

The degree of cross-immunity between human papillomavirus (HPV) types is fundamental both to the epidemiological dynamics of HPV and to the impact of HPV vaccination. Epidemiological data on HPV infections has been repeatedly interpreted as inconsistent with cross-immunity.

METHODS

We reevaluate the epidemiological data using a model to determine the odds ratios of multiple to single infections expected in the presence or absence of cross-immunity. We simulate a virtual longitudinal survey to determine the effect cross-immunity has on the prevalence of multiple infections. We calibrate our model to epidemiological data and estimate the extent of type replacement following vaccination against specific HPV types.

RESULTS

We find that cross-immunity can produce odds ratios of infection comparable with epidemiological observations. We show that the sample sizes underlying existing surveys have been insufficient to identify even intense cross-immunity. We also find that the removal of HPV type 16, type 18, and types 6 and 11 would increase the prevalence of nontargeted types by 50%, 29%, and 183%, respectively.

CONCLUSIONS

Cross-immunity between HPV types is consistent with epidemiological data, contrary to previous interpretations. Cross-immunity may cause significant type replacement following vaccination, and therefore should be considered in future vaccine studies and epidemiological models.

Potential overestimation of HPV vaccine impact due to unmasking of non-vaccine types: quantification using a multi-type mathematical model

INTRODUCTION

Estimates of human papillomavirus (HPV) vaccine impact in clinical trials and modelling studies rely on DNA tests of cytology or biopsy specimens to determine the HPV type responsible for a cervical lesion. DNA of several oncogenic HPV types may be detectable in a specimen. However, only one type may be responsible for a particular cervical lesion. Misattribution of the causal HPV type for a particular abnormality may give rise to an apparent increase in disease due to non-vaccine HPV types following vaccination ("unmasking").

METHODS

To investigate the existence and magnitude of unmasking, we analysed data from residual cytology and biopsy specimens in English women aged 20-64 years old using a stochastic type-specific individual-based model of HPV infection, progression and disease. The model parameters were calibrated to data on the prevalence of HPV DNA and cytological lesion of different grades, and used to assign causal HPV types to cervical lesions. The difference between the prevalence of all disease due to non-vaccine HPV types, and disease due to non-vaccine HPV types in the absence of vaccine HPV types, was then estimated.

RESULTS

There could be an apparent maximum increase of 3-10% in long-term cervical cancer incidence due to non-vaccine HPV types following vaccination.

CONCLUSION

Unmasking may be an important phenomenon in HPV post-vaccination epidemiology, in the same way that has been observed following pneumococcal conjugate vaccination.

Evolutionary ecology of human papillomavirus: trade-offs, coexistence, and origins of high-risk and low-risk types

BACKGROUND

We address the ecological and evolutionary dynamics of human papillomavirus (HPV) that lead to the dichotomy between high-risk (HR) and low-risk (LR) types. We hypothesize that HPV faces an evolutionary tradeoff between persistence and per-contact transmission probability. High virion production enhances transmissibility but also provokes an immune response leading to clearance and limited persistence. Alternatively, low virion production increases persistence at the cost of diminished transmission probability per sexual contact. We propose that LR HPV types use the former strategy and that HR types use the latter. Sexual behaviors in a host population determine the success of each strategy.

METHODS

We develop an evolutionary model of HPV epidemiology, which includes host sexual behavior, and we find evolutionarily stable strategies of HPV.

RESULTS

A slow turnover of sexual partners favors HR HPV, whereas high frequency of partner turnover selects for LR. When both sexual behaviors exist as subcultures in a population, disruptive selection can result in the coevolution and ecological coexistence of both HR and LR HPV types.

CONCLUSIONS

Our results indicate that the elimination of HR HPV through vaccines may alter the evolutionary trajectory of the remaining types and promote evolution of new HR HPV types.

Time for change? An economic evaluation of integrated cervical screening and HPV immunization programs in Canada

Many jurisdictions have implemented universal human papillomavirus (HPV) immunization programs in preadolescent females. However, the cost-effectiveness of modified cervical screening guidelines and/or catch-up immunization in older females in Canada has not been evaluated. We conducted a cost-utility analysis of screening and immunization with the bivalent vaccine for the Canadian setting from the Ministry of Health perspective. We used a dynamic model to capture herd immunity and included cross-protection against strains not included in the vaccine. We found that adding catch-up immunization to the current program would be cost-effective, and that combining catch-up immunization with delaying the age at which screening is first initiated could result in cost savings and net health gains.

The role of optimal control in assessing the most cost-effective implementation of a vaccination programme: HPV as a case study

Vaccination against the human papillomavirus (HPV) is a recent development in the UK. This paper uses an optimal control model to explore how best to target vaccination. We find that the vaccination of sexually active individuals has a greater impact on disease control than the vaccination of sexually non-active individuals. Extending the model to include male vaccination, we find that including males in a vaccination strategy is cost-effective. We compare the optimal control solution to that from a constant control model and show that the optimal control model is more efficient at forcing the system to a disease-controlled steady state.

The cost effectiveness of a quadrivalent human papillomavirus vaccine (6/11/16/18) in Hungary

OBJECTIVE

A transmission dynamic model was used to assess the epidemiological and economic impact of a quadrivalent human papillomavirus (HPV) (6/11/16/18) vaccine in preventing cervical cancer, cervical intraepithelial neoplasia grades 2 and 3 (CIN 2/3), CIN 1 and genital warts in Hungary.

METHODS

The routine vaccination of 12-year-old girls and the routine vaccination of 12-year-old girls plus a temporary catch-up programme for girls and women aged 12-24 years was evaluated.

RESULTS

The model projected that at year 100, both strategies could reduce the incidence of HPV 6/11/16/18-related cervical cancer, CIN 2/3, CIN 1 and genital warts cases among Hungarian women by 90%, 90%, 85% and 93%, respectively. Twenty-five years after the introduction of HPV vaccination in the population, routine vaccination of girls by the age of 12 reduced the cumulative number of cases of cervical cancer, CIN 2/3, CIN 1 and genital warts by 685, 13,473, 3,423 and 163,987, respectively. The incremental cost-effectiveness ratios of the two vaccination strategies were €9,577 and €10,646 per quality-adjusted life-year (QALY) gained over a time horizon of 100 years.

KEY LIMITATIONS

The model did not account for the health and economic impact of other HPV diseases which may result from HPV 16, 18, 6, and 11 infections such as vaginal, vulvar, penile, anal and head-neck cancers, and recurrent respiratory papillomatosis. Epidemiological data from Hungary on these other HPV diseases as well genital warts are needed.

CONCLUSION

A quadrivalent HPV vaccination programme can reduce the incidence of cervical cancer, CIN and genital warts in Hungary at a cost-per-QALY ratio within the range defined as cost effective.

When do sexual partnerships need to be accounted for in transmission models of human papillomavirus?

Human papillomavirus (HPV) is often transmitted through sexual partnerships. However, many previous HPV transmission models ignore the existence of partnerships by implicitly assuming that each new sexual contact is made with a different person. Here, we develop a simplified pair model—based on the example of HPV—that explicitly includes sexual partnership formation and dissolution. We show that not including partnerships can potentially result in biased projections of HPV prevalence. However, if transmission rates are calibrated to match empirical pre-vaccine HPV prevalence, the projected prevalence under a vaccination program does not vary significantly, regardless of whether partnerships are included.

Age-based programs for vaccination against HPV

BACKGROUND

The risk of infection with human papillomavirus (HPV) increases with age. Answering the question of which age groups are appropriate to target for catch-up vaccination with the newly licensed quadrivalent HPV vaccine (types 6/11/16/18) will be important for developing vaccine policy recommendations.

OBJECTIVES

To assess the value of varying female HPV vaccination strategies by specific age groups of a catch-up program in the United States.

METHODS

The authors used previously published mathematical population dynamic model and cost-utility analysis to evaluate the public health impact and cost-effectiveness of alternative quadrivalent HPV (6/11/16/18) vaccination strategies. The model simulates heterosexual transmission of HPV infection and occurrence of cervical intraepithelial neoplasia (CIN), cervical cancer, and external genital warts in an age-structured population stratified by sex and sexual activity groups. The cost-utility analysis estimates the cost of vaccination, screening, diagnosis, and treatment of HPV diseases, and quality-adjusted survival.

RESULTS

Compared with the current screening practices, vaccinating girls and women ages 12 to 24 years was the most effective strategy, reducing the number of HPV6/11/16/18-related genital warts, CIN grades 2 and 3, and cervical cancer cases among women in the next 25 years by 3,049,285, 1,399,935, and 30,021; respectively. The incremental cost-effectiveness ratio of this strategy when compared with vaccinating girls and women ages 12 to 19 years was $10,986 per quality-adjusted life-year gained. CONCLUSION;: Relative to other commonly accepted health-care programs, vaccinating girls and women ages 12 to 24 years appears cost-effective.

Latent coinfection and the maintenance of strain diversity

Technologies for strain differentiation and typing have made it possible to detect genetic diversity of pathogens, both within individual hosts and within communities. Coinfection of a host by more than one pathogen strain may affect the relative frequency of these strains at the population level through complex within- and between-host interactions; in infectious diseases that have a long latent period, interstrain competition during latency is likely to play an important role in disease dynamics. We show that SEIR models that include a class of latently coinfected individuals can have markedly different long-term dynamics than models without coinfection, and that coinfection can greatly facilitate the stable coexistence of strains. We demonstrate these dynamics using a model relevant to tuberculosis in which people may experience latent coinfection with both drug sensitive and drug resistant strains. Using this model, we show that the existence of a latent coinfected state allows the possibility that disease control interventions that target latency may facilitate the emergence of drug resistance.

Integrating epidemiology, psychology, and economics to achieve HPV vaccination targets

Human papillomavirus (HPV) vaccines provide an opportunity to reduce the incidence of cervical cancer. Optimization of cervical cancer prevention programs requires anticipation of the degree to which the public will adhere to vaccination recommendations. To compare vaccination levels driven by public perceptions with levels that are optimal for maximizing the community's overall utility, we develop an epidemiological game-theoretic model of HPV vaccination. The model is parameterized with survey data on actual perceptions regarding cervical cancer, genital warts, and HPV vaccination collected from parents of vaccine-eligible children in the United States. The results suggest that perceptions of survey respondents generate vaccination levels far lower than those that maximize overall health-related utility for the population. Vaccination goals may be achieved by addressing concerns about vaccine risk, particularly those related to sexual activity among adolescent vaccine recipients. In addition, cost subsidizations and shifts in federal coverage plans may compensate for perceived and real costs of HPV vaccination to achieve public health vaccination targets.

No coexistence for free: neutral null models for multistrain pathogens

In most pathogens, multiple strains are maintained within host populations. Quantifying the mechanisms underlying strain coexistence would aid public health planning and improve understanding of disease dynamics. We argue that mathematical models of strain coexistence, when applied to indistinguishable strains, should meet criteria for both ecological neutrality and population genetic neutrality. We show that closed clonal transmission models which can be written in an "ancestor-tracing" form that meets the former criterion will also satisfy the latter. Neutral models can be a parsimonious starting point for studying mechanisms of strain coexistence; implications for past and future studies are discussed.

Human papillomavirus vaccination: what is the best choice? A comparison of 16 strategies by means of a decisional model

Some European countries decided to include human papillomavirus (HPV) vaccines in national immunization schedules. In order to help decision makers choose the best vaccination policy for females, a decisional model has been developed. The study was performed from the National Health Service perspective. Several hypotheses of multi-cohort vaccination policies were compared. ‘Potentially avoidable infections’ were chosen as the outcome. The model envisioned a short-term scenario (2008–2011). The best policy was that of vaccinating 12-year-olds and, a year later, those aged 14–16 years; the most expensive strategy was that of vaccinating 12-year-old females and, after 1 year, vaccinating those aged 15, 18 and 25 years. The sensitivity analysis showed that coverage rate has a great effect on the cost of avoidable infections. The study offers stake-holders an important datum-point for the choice of the best HPV policy vaccination in the short term. Indeed, it could generate interesting savings for the National Health Service and a rapid HPV immunization of young girls.

A multi-type HPV transmission model

A prophylactic quadrivalent (types 6/11/16/18) vaccine against oncogenic and warts-causing genital Human papillomavirus (HPV) types was approved by the US Food and Drug Administration in 2006. This paper presents a nonlinear, deterministic, age-structured, mathematical model of the transmission dynamics of HPV and disease occurrence in a US population stratified by gender and sexual activity group. The model can assess both the epidemiologic consequences and cost effectiveness of alternative vaccination strategies in a setting of organized cervical cancer screening in the United States. Inputs for the model were obtained from public data sources, published literature, and analyses of clinical trial data. The results suggest that a prophylactic quadrivalent HPV vaccine can: (i) substantially reduce the incidence of disease, (ii) increase survival among females, (iii) improve quality of life for both males and females, (iv) be cost-effective when administered to females age 12-24 years, and (v) be cost-effective when implemented as a strategy that combines vaccination of both females and males before age 12 vaccination with a 12 to 24 years of age catch-up vaccination program.

Of mice and men: asymmetric interactions between Bordetella pathogen species

In a recent experiment, we found that mice previously infected with Bordetella pertussis were not protected against a later infection with Bordetella parapertussis, while primary infection with B. parapertussis conferred cross-protection. This challenges the common assumption made in most mathematical models for pathogenic strain dynamics that cross-immunity between strains is symmetric. Here we investigate the potential consequences of this pattern on the circulation of the two pathogens in human populations. To match the empirical dominance of B. pertussis, we made the additional assumption that B. parapertussis pays a cost in terms of reduced fitness. We begin by exploring the range of parameter values that allow the coexistence of the two pathogens, with or without vaccination. We then track the dynamics of the system following the introduction of anti-pertussis vaccination. Our results suggest that (1) in order for B. pertussis to be more prevalent than B. parapertussis, the former must have a strong competitive advantage, possibly in the form of higher infectivity, and (2) because of asymmetric cross-immunity, the introduction of anti-pertussis vaccination should have little effect on the absolute prevalence of B. parapertussis. We discuss the evidence supporting these predictions, and the potential relevance of this model for other pathogens.