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We aimed to quantify the health impact of immediate introduction of a single-dose human papillomavirus (HPV) vaccination program in a high-burden setting, as waiting until forthcoming trials are completed to implement single-dose HPV vaccination may result in health losses, particularly for cohorts who would age-out of vaccination eligibility. Two mathematical models fitted to a high-burden setting projected cervical cancer incidence rates associated with (a) immediate implementation of one-dose HPV vaccination vs (b) waiting 5 years for evidence from randomized trials to determine if one- or two-doses should be implemented. We conducted analyses assuming a single dose was either noninferior or inferior to two doses. The models projected that immediate implementation of a noninferior single-dose vaccine led to a 7.2% to 9.6% increase in cancers averted between 2021 to 2120, compared to waiting 5 years. Health benefits remained greater with immediate implementation despite an inferior single-dose efficacy (80%), but revaccination of one-dose recipients became more important assuming vaccine waning. Under most circumstances, immediate vaccination avoided health losses for those aging out of vaccine eligibility, leading to greater health benefits than waiting for more information in 5 years.

Background: Inequalities in cervical cancer may be increased following mass vaccination against the human papillomavirus (HPV) if girls with low vaccine uptake also have low future participation in cervical cancer screening. We evaluated how vaccine uptake distribution affects inequalities in squamous cell carcinoma (SCC) incidence between groups with different screening participation.Methods: We used an individual-based transmission dynamic model of HPV infection and disease (HPV-ADVISE). Females were stratified by routine screening frequency. We modeled the impact of vaccination on SCC incidence rate differences (absolute inequality) and incidence rate ratios (relative inequality) between women who have routine screening intervals of Results: Absolute SCC inequalities between groups with different screening rates were predicted to decrease after vaccination, even when women with the lowest screening participation had the lowest vaccine uptake. Herd effects helped reduce absolute inequalities when vaccine uptake was unequal. Conversely, relative SCC inequalities remained unchanged or increased after vaccination. Results were robust to different overall vaccination coverages and sexual mixing scenarios.Conclusion: Though mass HPV vaccination is predicted to substantially decrease SCC incidence rates, never screened women will still have the highest disease burden after vaccination.Impact: To reduce both absolute and relative SCC inequalities, public health initiatives will need to address inequalities in both vaccine uptake and in cervical cancer screening participation. Cancer Epidemiol Biomarkers Prev; 24(1); 276–85. ©2014 AACR.

Supplementary Figure S2. Pre- and post-vaccination inequalities between screening behavior levels with shorter vaccine duration.

Heterogeneity in the number of lifetime/recent partners among women participating in PISCES

Background: Papanicolaou smear screening has significantly reduced cervical cancer morbidity and mortality. However, inequalities still persist across different socioeconomic status (SES) groups. These inequalities have been associated with differential participation in screening. However, even with equal participation to screening, some women may still have greater risk of cervical cancer because of sexual behavior. We aim to identify the sociodemographic characteristics of women who reported greater sexual activity and/or screening underuse.Methods: We used data from (i) the Canadian Community Health Survey—2005, a population-based survey of 130,000 Canadians, and (ii) a multicenter study including 952 women screened for cervical cancer.Results: Aboriginals and women with lower SES reported greater sexual activity and lower screening participation, which may produce synergetic effects toward higher cervical cancer risk. Women who did not complete high school and aboriginals were, respectively, 3.6 and 2.5 times more likely to report sexual debut before 15 years old compared with women with university degree and Caucasians. Women who did not complete high school were 2.2 times more likely to have never been screened compared with women with university degree. East and South Asian women were, respectively, 4.3 and 3.1 times more likely to have never been screened than Canadian-born women but reported lower levels of sexual activity and were adherent to screening guidelines when screened at least once.Conclusions: The success of human papillomavirus vaccination at reducing cervical cancer and inequalities will depend on achieving high coverage among high-risk subpopulations.Impact: These groups must be monitored closely, and if need be, targeted for additional interventions. Cancer Epidemiol Biomarkers Prev; 22(4); 641–52. ©2013 AACR.

Socio-demographic characteristics associated with sexual activity of women aged 25 to 44 recruited in PISCES (n=496)

BACKGROUND: The WHO Strategic Advisory Group of Experts recommended that an extended interval of 3-5 years between the two doses of the human papillomavirus (HPV) vaccine could be considered to alleviate vaccine supply shortages. However, three concerns have limited the introduction of extended schedules: girls could be infected between the two doses, the vaccination coverage for the second dose could be lower at ages 13-14 years than at ages 9-10 years, and identifying girls vaccinated with a first dose to give them the second dose could be difficult. Using mathematical modelling, we examined the potential effect of these concerns on the population-level impact and efficiency of extended dose HPV vaccination schedules. METHODS: We used HPV-ADVISE, an individual-based, transmission-dynamic model of multitype HPV infection and disease, calibrated to country-specific data for four low-income and middle-income countries (India, Viet Nam, Uganda, and Nigeria). For the extended dose scenarios, we varied the vaccination coverage of the second dose among girls previously vaccinated, the one-dose vaccine efficacy, and the one-dose vaccine duration of protection. We also examined a strategy in which girls aged 14 years were vaccinated irrespective of their previous vaccination status. We used a scenario of girls-only two-dose vaccination at age 9 years (vaccine=9 valent, vaccine-type efficacy=100%, duration of protection=lifetime, and coverage=80%) as our comparator. We estimated two outcomes: the relative reduction in the age-standardised cervical cancer incidence (population-level impact) and the number of cervical cancers averted per 100 000 doses (efficiency). FINDINGS: Our model projected substantial reductions in cervical cancer incidence over 100 years with the two-dose schedule (79-86% depending on the country), compared with no vaccination. Projections for the 5-year extended schedule, in which the second dose is given only to girls previously vaccinated at age 9 years, were similar to the current two-dose schedule, unless vaccination coverage of the second dose is very low (reductions in cervical cancer incidence of 71-78% assuming 30% coverage at age 14 years among girls vaccinated at age 9 years). However, when the dose at age 14 years is given to girls irrespective of vaccination status and assuming high vaccination coverage, the model projected a substantially greater reduction in cervical cancer incidence compared with the current two-dose schedule (reductions in cervical cancer incidence of 86-93% assuming 70% coverage at age 14 years, irrespective of vaccination status). Efficiency of the extended schedule was greater than the two-dose schedule, even with a drop in vaccination coverage. INTERPRETATION: The three concerns are unlikely to have a substantial effect on the population-level impact of extended dose schedules. Hence, extended dose schedules will likely provide similar cervical cancer reductions as two-dose schedules, while reducing the number of doses required in the short-term, providing a more efficient use of scarce resources, and offering a 5-year time window to reassess the necessity of the second dose. FUNDING: WHO, Canadian Institute of Health Research Foundation, Fonds de recherche du Québec-Santé, Digital Research Alliance of Canada, and Bill & Melinda Gates Foundation.

Background We estimated the lifetime medical costs attributable to sexually transmitted infections (STIs) acquired in 2018, including sexually acquired human immunodeficiency virus (HIV). Methods We estimated the lifetime medical costs of infections acquired in 2018 in the United States for 8 STIs: chlamydia, gonorrhea, trichomoniasis, syphilis, genital herpes, human papillomavirus (HPV), hepatitis B, and HIV. We limited our analysis to lifetime medical costs incurred for treatment of STIs and for treatment of related sequelae; we did not include other costs, such as STI prevention. For each STI, except HPV, we calculated the lifetime medical cost by multiplying the estimated number of incident infections in 2018 by the estimated lifetime cost per infection. For HPV, we calculated the lifetime cost based on the projected lifetime incidence of health outcomes attributed to HPV infections acquired in 2018. Future costs were discounted at 3% annually. Results Incident STIs in 2018 imposed an estimated $15.9 billion (25th-75th percentile: $14.9-16.9 billion) in discounted, lifetime direct medical costs (2019 US dollars). Most of this cost was due to sexually acquired HIV ($13.7 billion) and HPV ($0.8 billion). STIs in women accounted for about one fourth of the cost of incident STIs when including HIV, but about three fourths when excluding HIV. STIs among 15- to 24-year-olds accounted for $4.2 billion (26%) of the cost of incident STIs. Conclusions Incident STIs continue to impose a considerable lifetime medical cost burden in the United States. These results can inform health economic analyses to promote the use of cost-effective STI prevention interventions to reduce this burden.

Introduction Human papillomavirus (HPV) can cause anogenital warts and several types of cancer, including cervical cancers and precancers. We estimated the prevalence, incidence, and number of persons with prevalent and incident HPV infections in the United States in 2018. Methods Prevalence and incidence were estimated for infections with any HPV (any of 37 types detected using Linear Array) and disease-associated HPV, 2 types that cause anogenital warts plus 14 types detected by tests used for cervical cancer screening (HPV 6/11/16/18/31/33/35/39/45/51/52/56/58/59/66/68). We used the 2013-2016 National Health and Nutrition Examination Survey to estimate prevalence among 15- to 59-year-olds, overall and by sex. Incidences in 2018 were estimated per 10,000 persons using an individual-based transmission-dynamic type-specific model calibrated to US data. We estimated number of infected persons by applying prevalences and incidences to 2018 US population estimates. Results Prevalence of infection with any HPV was 40.0% overall, 41.8% in men, and 38.4% in women; prevalence of infection with disease-associated HPV was 24.2% in men and 19.9% in women. An estimated 23.4 and 19.2 million men and women had a disease-associated HPV type infection in 2018. Incidences of any and disease-associated HPV infection were 1222 and 672 per 10,000 persons; incidence of disease-associated HPV infection was 708 per 10,000 men and 636 per 10,000 women. An estimated 6.9 and 6.1 million men and women had an incident infection with a disease-associated HPV type in 2018. Conclusions We document a high HPV burden of infection in the United States in 2018, with 42 million persons infected with disease-associated HPV and 13 million persons acquiring a new infection. Although most infections clear, some disease-associated HPV type infections progress to disease. The HPV burden highlights the need for continued monitoring of HPV-associated cancers, cervical cancer screening, and HPV vaccination to track and prevent disease.

Summary Background WHO is developing a global strategy towards eliminating cervical cancer as a public health problem, which proposes an elimination threshold of four cases per 100 000 women and includes 2030 triple-intervention coverage targets for scale-up of human papillomavirus (HPV) vaccination to 90%, twice-lifetime cervical screening to 70%, and treatment of pre-invasive lesions and invasive cancer to 90%. We assessed the impact of achieving the 90–70–90 triple-intervention targets on cervical cancer mortality and deaths averted over the next century. We also assessed the potential for the elimination initiative to support target 3.4 of the UN Sustainable Development Goals (SDGs)—a one-third reduction in premature mortality from non-communicable diseases by 2030. Methods The WHO Cervical Cancer Elimination Modelling Consortium (CCEMC) involves three independent, dynamic models of HPV infection, cervical carcinogenesis, screening, and precancer and invasive cancer treatment. Reductions in age-standardised rates of cervical cancer mortality in 78 low-income and lower-middle-income countries (LMICs) were estimated for three core scenarios: girls-only vaccination at age 9 years with catch-up for girls aged 10–14 years; girls-only vaccination plus once-lifetime screening and cancer treatment scale-up; and girls-only vaccination plus twice-lifetime screening and cancer treatment scale-up. Vaccination was assumed to provide 100% lifetime protection against infections with HPV types 16, 18, 31, 33, 45, 52, and 58, and to scale up to 90% coverage in 2020. Cervical screening involved HPV testing at age 35 years, or at ages 35 years and 45 years, with scale-up to 45% coverage by 2023, 70% by 2030, and 90% by 2045, and we assumed that 50% of women with invasive cervical cancer would receive appropriate surgery, radiotherapy, and chemotherapy by 2023, which would increase to 90% by 2030. We summarised results using the median (range) of model predictions. Findings In 2020, the estimated cervical cancer mortality rate across all 78 LMICs was 13·2 (range 12·9–14·1) per 100 000 women. Compared to the status quo, by 2030, vaccination alone would have minimal impact on cervical cancer mortality, leading to a 0·1% (0·1–0·5) reduction, but additionally scaling up twice-lifetime screening and cancer treatment would reduce mortality by 34·2% (23·3–37·8), averting 300 000 (300 000–400 000) deaths by 2030 (with similar results for once-lifetime screening). By 2070, scaling up vaccination alone would reduce mortality by 61·7% (61·4–66·1), averting 4·8 million (4·1–4·8) deaths. By 2070, additionally scaling up screening and cancer treatment would reduce mortality by 88·9% (84·0–89·3), averting 13·3 million (13·1–13·6) deaths (with once-lifetime screening), or by 92·3% (88·4–93·0), averting 14·6 million (14·1–14·6) deaths (with twice-lifetime screening). By 2120, vaccination alone would reduce mortality by 89·5% (86·6–89·9), averting 45·8 million (44·7–46·4) deaths. By 2120, additionally scaling up screening and cancer treatment would reduce mortality by 97·9% (95·0–98·0), averting 60·8 million (60·2–61·2) deaths (with once-lifetime screening), or by 98·6% (96·5–98·6), averting 62·6 million (62·1–62·8) deaths (with twice-lifetime screening). With the WHO triple-intervention strategy, over the next 10 years, about half (48% [45–55]) of deaths averted would be in sub-Saharan Africa and almost a third (32% [29–34]) would be in South Asia; over the next 100 years, almost 90% of deaths averted would be in these regions. For premature deaths (age 30–69 years), the WHO triple-intervention strategy would result in rate reductions of 33·9% (24·4–37·9) by 2030, 96·2% (94·3–96·8) by 2070, and 98·6% (96·9–98·8) by 2120. Interpretation These findings emphasise the importance of acting immediately on three fronts to scale up vaccination, screening, and treatment for pre-invasive and invasive cervical cancer. In the next 10 years, a one-third reduction in the rate of premature mortality from cervical cancer in LMICs is possible, contributing to the realisation of the 2030 UN SDGs. Over the next century, successful implementation of the WHO elimination strategy would reduce cervical cancer mortality by almost 99% and save more than 62 million women's lives. Funding WHO, UNDP, UN Population Fund, UNICEF–WHO–World Bank Special Program of Research, Development and Research Training in Human Reproduction, Germany Federal Ministry of Health, National Health and Medical Research Council Australia, Centre for Research Excellence in Cervical Cancer Control, Canadian Institute of Health Research, Compute Canada, and Fonds de recherche du Quebec–Sante.

Summary Background The WHO Director-General has issued a call for action to eliminate cervical cancer as a public health problem. To help inform global efforts, we modelled potential human papillomavirus (HPV) vaccination and cervical screening scenarios in low-income and lower-middle-income countries (LMICs) to examine the feasibility and timing of elimination at different thresholds, and to estimate the number of cervical cancer cases averted on the path to elimination. Methods The WHO Cervical Cancer Elimination Modelling Consortium (CCEMC), which consists of three independent transmission-dynamic models identified by WHO according to predefined criteria, projected reductions in cervical cancer incidence over time in 78 LMICs for three standardised base-case scenarios: girls-only vaccination; girls-only vaccination and once-lifetime screening; and girls-only vaccination and twice-lifetime screening. Girls were vaccinated at age 9 years (with a catch-up to age 14 years), assuming 90% coverage and 100% lifetime protection against HPV types 16, 18, 31, 33, 45, 52, and 58. Cervical screening involved HPV testing once or twice per lifetime at ages 35 years and 45 years, with uptake increasing from 45% (2023) to 90% (2045 onwards). The elimination thresholds examined were an average age-standardised cervical cancer incidence of four or fewer cases per 100 000 women-years and ten or fewer cases per 100 000 women-years, and an 85% or greater reduction in incidence. Sensitivity analyses were done, varying vaccination and screening strategies and assumptions. We summarised results using the median (range) of model predictions. Findings Girls-only HPV vaccination was predicted to reduce the median age-standardised cervical cancer incidence in LMICs from 19·8 (range 19·4–19·8) to 2·1 (2·0–2·6) cases per 100 000 women-years over the next century (89·4% [86·2–90·1] reduction), and to avert 61·0 million (60·5–63·0) cases during this period. Adding twice-lifetime screening reduced the incidence to 0·7 (0·6–1·6) cases per 100 000 women-years (96·7% [91·3–96·7] reduction) and averted an extra 12·1 million (9·5–13·7) cases. Girls-only vaccination was predicted to result in elimination in 60% (58–65) of LMICs based on the threshold of four or fewer cases per 100 000 women-years, in 99% (89–100) of LMICs based on the threshold of ten or fewer cases per 100 000 women-years, and in 87% (37–99) of LMICs based on the 85% or greater reduction threshold. When adding twice-lifetime screening, 100% (71–100) of LMICs reached elimination for all three thresholds. In regions in which all countries can achieve cervical cancer elimination with girls-only vaccination, elimination could occur between 2059 and 2102, depending on the threshold and region. Introducing twice-lifetime screening accelerated elimination by 11–31 years. Long-term vaccine protection was required for elimination. Interpretation Predictions were consistent across our three models and suggest that high HPV vaccination coverage of girls can lead to cervical cancer elimination in most LMICs by the end of the century. Screening with high uptake will expedite reductions and will be necessary to eliminate cervical cancer in countries with the highest burden. Funding WHO, UNDP, UN Population Fund, UNICEF–WHO–World Bank Special Program of Research, Development and Research Training in Human Reproduction, Canadian Institute of Health Research, Fonds de recherche du Quebec–Sante, Compute Canada, National Health and Medical Research Council Australia Centre for Research Excellence in Cervical Cancer Control.

Summary Background To eliminate cervical cancer as a public health problem, WHO currently recommends routine vaccination of adolescent girls with two doses of the human papillomavirus (HPV) vaccine before sexual debut. However, many countries have yet to implement this because of financial or logistical barriers to delivering two doses outside the infant immunisation programme. Methods Using three independent HPV transmission models, we estimated the long-term health benefits and cost-effectiveness of one-dose versus two-dose HPV vaccination, in 192 countries, assuming that one dose of the vaccine gives either a shorter duration of full protection (20 or 30 years) or lifelong protection but lower vaccine efficacy (e.g., 80%) compared to two doses. We simulated routine vaccination with the 9-valent HPV vaccine in 10-year-old girls at 80% coverage for the years 2021–2120, with a one-year catch-up of 80% 11–14-year-old girls on the first year of the programme. Findings Over the next century, one-dose vaccination at 80% coverage could avert 64 million (80%UI 62·2–64·8) and 66·6 million (80%UI 63·4–69·1) cervical cancer cases should one dose of the vaccine confer 20 and 30 years of protection, respectively. Should one dose of the vaccine provide lifelong protection at 80% vaccine efficacy, 68·4 million (80%UI 63·8–69·4) cervical cancer cases could be prevented. Across all country income groups, two-dose schedules conferring lifelong protection would avert only slightly more cases (2·1–8·7 million) than the one-dose scenarios explored. Around 330 to 5230 additional girls need to be vaccinated with the second dose to prevent one cervical cancer case, depending on the epidemiological profiles of the country. Interpretation Results were consistent across the three independent models and suggest that one-dose vaccination has similar health benefits to a two-dose programme while simplifying vaccine delivery, reducing costs and alleviating vaccine supply constraints. Funding Bill & Melinda Gates Foundation Research in context Evidence before this study Primary prevention of cervical cancer is now available with human papillomavirus (HPV) vaccination. Initially administered as a three-dose regimen, the HPV vaccine schedule recommended by WHO has now switched to two doses for individuals below the age of 15 years. Although WHO recommends all countries to routinely immunise adolescent girls with two doses, many low- and middle-income countries, with high disease burden, have yet to implement national HPV vaccination programmes because of the challenges of delivering two vaccine doses to adolescent females. Recently, HPV vaccine implementation in many countries has been further delayed due to constraints in vaccine supply and difficulties in access during COVID-19 epidemics. These financial, logistical, and supply constraints have motivated research into one-dose vaccination schedules. Evidence emerging from trials and observational studies suggests that one dose may also provide a high level of protection against incident and persistent HPV infections. If proven effective, the one-dose HPV vaccination schedule would simplify vaccine delivery and lower costs of national vaccination programmes, potentially enabling more countries to implement one and as a result, facilitating global cervical cancer prevention. We searched PubMed for trials, cohort and modelling studies published in 2018 and 2020, with the terms “(health impact OR impact OR modelling OR cost-effectiveness OR CEA OR durability OR effectiveness) AND (HPV OR human papillomavirus OR cervical cancer)” and identified 151 results. Ten published articles—four trials, three cohort studies, two modelling analyses, one systematic review of trials—evaluated the population impact of one dose of the vaccine on cervical cancer disease outcome among females and all studies showed one dose of the vaccine might be as effective as two doses in preventing HPV infection. However as the trials and cohorts were single-country studies in select populations, the global impact remains unknown. Both published modelling analyses only used one model to estimate the impact of one-dose vaccination, and only examined a few countries. To our knowledge, no published article has modelled the global impact of routine one-dose vaccination on cervical cancer prevention by synthesising the results from more than one model. Added value of this study This study presents the first evidence on the potential global impact of a routine one-dose regimen, from a comparative modelling analysis that synthesises results from three published dynamic models calibrated to countries with varying epidemiological and demographic profiles. We found consistent results across all models suggesting that routine one-dose vaccination provides the majority of health benefits to the two-dose programme should a single dose of the vaccine confer more than 20 years of protection at full potential efficacy or 80% efficacy with lifelong protection. Implications of all the available evidence Findings suggest that routine one-dose vaccinations could avert almost as many cervical cancer cases as a two-dose programme. The one-dose regimen would be cheaper and easier to implement for most countries while alleviating vaccine supply constraints. To cope with the COVID-19 pandemic, many governments have had to implement stringent physical distancing measures, which has led to the suspension of routine immunisation programmes. Public health authorities grapple with the logistic challenges of delivering immunisation services while minimising the risk of SARS-CoV-2 transmission. Compared to the two-dose vaccination schedule, a one-dose vaccination schedule would reduce interactions between vaccinees and health workers, simplifying vaccine delivery while also decreasing SARS-CoV-2 exposure.

Introduction We estimated the lifetime medical costs of diagnosed cases of diseases attributable to human papillomavirus (HPV) infections acquired in 2018. Methods We adapted an existing mathematical model of HPV transmission and associated diseases to estimate the lifetime number of diagnosed cases of disease (genital warts; cervical intraepithelial neoplasia; and cervical, vaginal, vulvar, penile, anal, and oropharyngeal cancers) attributable to HPV infections that were acquired in 2018. For each of these outcomes, we multiplied the estimated number of cases by the estimated lifetime medical cost per case obtained from previous studies. We estimated the costs of recurrent respiratory papillomatosis in a separate calculation. Future costs were discounted at 3% annually. Results The estimated discounted lifetime medical cost of diseases attributable to HPV infections acquired in 2018 among people aged 15 to 59 years was $774 million (in 2019 US dollars), of which approximately half was accounted for by infections in those aged 15 to 24 years. Human papillomavirus infections in women accounted for approximately 90% of the lifetime number of diagnosed cases of disease and 70% of the lifetime cost attributable to HPV infections acquired in 2018 among those aged 15 to 59 years. Conclusions We estimated the lifetime medical costs of diseases attributable to HPV infections acquired in 2018 to be $774 million. This estimate is lower than previous estimates, likely due to the impact of HPV vaccination. The lifetime cost of disease attributable to incident HPV infections is expected to decrease further over time as HPV vaccination coverage increases.

We estimated the lifetime medical costs attributable to sexually transmitted infections (STIs) acquired in 2018, including sexually acquired human immunodeficiency virus (HIV).We estimated the lifetime medical costs of infections acquired in 2018 in the United States for 8 STIs: chlamydia, gonorrhea, trichomoniasis, syphilis, genital herpes, human papillomavirus (HPV), hepatitis B, and HIV. We limited our analysis to lifetime medical costs incurred for treatment of STIs and for treatment of related sequelae; we did not include other costs, such as STI prevention. For each STI, except HPV, we calculated the lifetime medical cost by multiplying the estimated number of incident infections in 2018 by the estimated lifetime cost per infection. For HPV, we calculated the lifetime cost based on the projected lifetime incidence of health outcomes attributed to HPV infections acquired in 2018. Future costs were discounted at 3% annually.Incident STIs in 2018 imposed an estimated $15.9 billion (25th-75th percentile: $14.9-16.9 billion) in discounted, lifetime direct medical costs (2019 US dollars). Most of this cost was due to sexually acquired HIV ($13.7 billion) and HPV ($0.8 billion). STIs in women accounted for about one fourth of the cost of incident STIs when including HIV, but about three fourths when excluding HIV. STIs among 15- to 24-year-olds accounted for $4.2 billion (26%) of the cost of incident STIs.Incident STIs continue to impose a considerable lifetime medical cost burden in the United States. These results can inform health economic analyses to promote the use of cost-effective STI prevention interventions to reduce this burden.

We used transmission-dynamic modeling to estimate the added effectiveness of vaccinating multiple cohorts of females (12-26 years) in Australia compared with the theoretical introduction of routine-only (12-13 years) vaccination. Our results suggest that vaccinating multiple cohorts produced markedly faster direct/herd effects, and it added benefits that last for 20-70 years. Furthermore, the number needed to vaccinate to prevent 1 anogential warts (AGW) case or cervical cancer (CC) was similar for routine + catch-up (AGW = 9.9, CC = 678) and routine-only vaccination (AGW = 9.9, CC = 677), thus providing similar levels of efficiency per person vaccinated.

BACKGROUND We estimated the potential impact and cost-effectiveness of providing 3-doses of nonavalent human papillomavirus (HPV) vaccine (9vHPV) to females aged 13-18 years who had previously completed a series of quadrivalent HPV vaccine (4vHPV), a strategy we refer to as "additional 9vHPV vaccination." METHODS We used 2 distinct models: (1) the simplified model, which is among the most basic of the published dynamic HPV models, and (2) the US HPV-ADVISE model, a complex, stochastic, individual-based transmission-dynamic model. RESULTS When assuming no 4vHPV cross-protection, the incremental cost per quality-adjusted life-year (QALY) gained by additional 9vHPV vaccination was $146 200 in the simplified model and $108 200 in the US HPV-ADVISE model ($191 800 when assuming 4vHPV cross-protection). In 1-way sensitivity analyses in the scenario of no 4vHPV cross-protection, the simplified model results ranged from $70 300 to $182 000, and the US HPV-ADVISE model results ranged from $97 600 to $118 900. CONCLUSIONS The average cost per QALY gained by additional 9vHPV vaccination exceeded $100 000 in both models. However, the results varied considerably in sensitivity and uncertainty analyses. Additional 9vHPV vaccination is likely not as efficient as many other potential HPV vaccination strategies, such as increasing primary 9vHPV vaccine coverage.

For classical billiards, we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As examples of 2D chaotic billiards, we considered the Bunimovich stadium billiard and the Sinai billiard. In the level spacing distribution and spectral rigidity, we found GOE behaviour consistent with predictions from random matrix theory. We studied transport properties and computed a diffusion coefficient. For the Sinai billiard, we found normal diffusion, while the stadium billiard showed anomalous diffusion behaviour. As example of a 2D integrable billiard, we considered the rectangular billiard. We found very rigid behaviour with strongly correlated spectra similar to a Dirac comb. These findings present numerical evidence for universality in level spacing fluctuations to hold in classically integrable systems and in classically fully chaotic systems.

Background: Inequalities in cervical cancer may be increased following mass vaccination against the human papillomavirus (HPV) if girls with low vaccine uptake also have low future participation in cervical cancer screening. We evaluated how vaccine uptake distribution affects inequalities in squamous cell carcinoma (SCC) incidence between groups with different screening participation. Methods: We used an individual-based transmission dynamic model of HPV infection and disease (HPV-ADVISE). Females were stratified by routine screening frequency. We modeled the impact of vaccination on SCC incidence rate differences (absolute inequality) and incidence rate ratios (relative inequality) between women who have routine screening intervals of Results: Absolute SCC inequalities between groups with different screening rates were predicted to decrease after vaccination, even when women with the lowest screening participation had the lowest vaccine uptake. Herd effects helped reduce absolute inequalities when vaccine uptake was unequal. Conversely, relative SCC inequalities remained unchanged or increased after vaccination. Results were robust to different overall vaccination coverages and sexual mixing scenarios. Conclusion: Though mass HPV vaccination is predicted to substantially decrease SCC incidence rates, never screened women will still have the highest disease burden after vaccination. Impact: To reduce both absolute and relative SCC inequalities, public health initiatives will need to address inequalities in both vaccine uptake and in cervical cancer screening participation. Cancer Epidemiol Biomarkers Prev; 24(1); 276–85. ©2014 AACR.

BACKGROUND: In the United States, the routine age for human papillomavirus (HPV) vaccination is 11 to 12 years, with catch-up vaccination through age 26 years for women and 21 years for men. U.S. vaccination policy on use of the 9-valent HPV vaccine in adult women and men is being reviewed. OBJECTIVE: To evaluate the added population-level effectiveness and cost-effectiveness of extending the current U.S. HPV vaccination program to women aged 27 to 45 years and men aged 22 to 45 years. DESIGN: The analysis used HPV-ADVISE (Agent-based Dynamic model for VaccInation and Screening Evaluation), an individual-based transmission dynamic model of HPV infection and associated diseases, calibrated to age-specific U.S. data. DATA SOURCES: Published data. TARGET POPULATION: Women aged 27 to 45 years and men aged 22 to 45 years in the United States. TIME HORIZON: 100 years. PERSPECTIVE: Health care sector. INTERVENTION: 9-valent HPV vaccination. OUTCOME MEASURES: HPV-associated outcomes prevented and cost-effectiveness ratios. RESULTS OF BASE-CASE ANALYSIS: The model predicts that the current U.S. HPV vaccination program will reduce the number of diagnoses of anogenital warts and cervical intraepithelial neoplasia of grade 2 or 3 and cases of cervical cancer and noncervical HPV-associated cancer by 82%, 80%, 59%, and 39%, respectively, over 100 years and is cost saving (vs. no vaccination). In contrast, extending vaccination to women and men aged 45 years is predicted to reduce these outcomes by an additional 0.4, 0.4, 0.2, and 0.2 percentage points, respectively. Vaccinating women and men up to age 30, 40, and 45 years is predicted to cost $830 000, $1 843 000, and $1 471 000, respectively, per quality-adjusted life-year gained (vs. current vaccination). RESULTS OF SENSITIVITY ANALYSIS: Results were most sensitive to assumptions about natural immunity and progression rates after infection, historical vaccination coverage, and vaccine efficacy. LIMITATION: Uncertainty about the proportion of HPV-associated disease due to infections after age 26 years and about the level of herd effects from the current HPV vaccination program. CONCLUSION: The current HPV vaccination program is predicted to be cost saving. Extending vaccination to older ages is predicted to produce small additional health benefits and result in substantially higher incremental cost-effectiveness ratios than the current recommendation. PRIMARY FUNDING SOURCE: Centers for Disease Control and Prevention.

Randomized clinical trials are currently examining the efficacy of a nonavalent human papillomavirus (HPV) vaccine, including HPV-types 6/11/16/18/31/33/45/52/58. Evidence on the cost-effectiveness of the nonavalent is required for timely policy-decisions. We compared the potential cost-effectiveness of the nonavalent and quadrivalent HPV vaccines. We used a multi-type individual-based transmission-dynamic model of HPV infection and diseases, 70-year time-horizon, 3% discount rate and healthcare payer perspective. We calibrated the model to Canadian sexual behavior and epidemiologic data, and estimated Quality-Adjusted Life-Years (QALYs) lost and costs ($CAN 2010) from the literature. Under base-case assumptions (vaccinating 10-year-old girls, 80% coverage, 95$/dose, vaccine-type efficacy = 95%, cross-protection for the quadrivalent vaccine, duration of vaccine-type protection (cross-protection) = 20 (10) years), using the quadrivalent and nonavalent vaccines is estimated to cost $15,528 [12,056; 19,140] and $12,203 [9,331; 17,292] per QALY-gained, respectively. At equal price, the nonavalent vaccine is more cost-effective than the quadrivalent vaccine, even when assuming both shorter duration of protection (nonavalent = 20 years vs. quadrivalent = lifelong) and lower vaccine-type efficacy (nonavalent = 85% vs. quadrivalent = 95%). However, the additional cost per dose of the nonavalent vaccine should not exceed $11 to remain more cost-effective than the quadrivalent vaccine, and $24 to represent a cost-effective alternative to the quadrivalent vaccine (using a $40,000/QALY-gained threshold). The nonavalent vaccine can be a cost-effective alternative to the quadrivalent vaccine, even in scenarios where nonavalent vaccine efficacy is 85%. However, because most cervical cancers are caused by HPV-16/18, it is unlikely that the nonavalent would be used if its efficacy against these types is lower than current HPV vaccines.

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.

A recent clinical trial using the 9-valent human papillomavirus virus (HPV) vaccine has shown that antibody responses after 2 doses are noninferior to those after 3 doses, suggesting that 2 and 3 doses may have comparable vaccine efficacy. We used an individual-based transmission-dynamic model to compare the population-level effectiveness and cost-effectiveness of 2- and 3-dose schedules of 9-valent HPV vaccine in the United States. Our model predicts that if 2 doses of 9-valent vaccine protect for ≥20 years, the additional benefits of a 3-dose schedule are small as compared to those of 2-dose schedules, and 2-dose schedules are likely much more cost-efficient than 3-dose schedules.

We study chaotic behavior of a classical optical stadium billiard model. We construct a matrix of time-of-travel along trajectories corresponding to a set of boundary points. We carry out a level spacing fluctuation analysis and compute the Dyson–Mehta spectral rigidity. The distribution of time-of-travel is approximately described by a Gaussian. The results for level spacing distribution and spectral rigidity show universal behavior.

Background We conducted a systematic review of mathematical models of transmission dynamic of Clostridium difficile infection (CDI) in healthcare settings, to provide an overview of existing models and their assessment of different CDI control strategies. Methods We searched MEDLINE, EMBASE and Web of Science up to February 3, 2016 for transmission-dynamic models of Clostridium difficile in healthcare settings. The models were compared based on their natural history representation of Clostridium difficile, which could include health states (S-E-A-I-R-D: Susceptible-Exposed-Asymptomatic-Infectious-Resistant-Deceased) and the possibility to include healthcare workers and visitors (vectors of transmission). Effectiveness of interventions was compared using the relative reduction (compared to no intervention or current practice) in outcomes such as incidence of colonization, CDI, CDI recurrence, CDI mortality, and length of stay. Results Nine studies describing six different models met the inclusion criteria. Over time, the models have generally increased in complexity in terms of natural history and transmission dynamics and number/complexity of interventions/bundles of interventions examined. The models were categorized into four groups with respect to their natural history representation: S-A-I-R, S-E-A-I, S-A-I, and S-E-A-I-R-D. Seven studies examined the impact of CDI control strategies. Interventions aimed at controlling the transmission, lowering CDI vulnerability and reducing the risk of recurrence/mortality were predicted to reduce CDI incidence by 3–49%, 5–43% and 5–29%, respectively. Bundles of interventions were predicted to reduce CDI incidence by 14–84%. Conclusions Although CDI is a major public health problem, there are very few published transmission-dynamic models of Clostridium difficile. Published models vary substantially in the interventions examined, the outcome measures used and the representation of the natural history of Clostridium difficile, which make it difficult to synthesize results and provide a clear picture of optimal intervention strategies. Future modeling efforts should pay specific attention to calibration, structural uncertainties, and transparent reporting practices.

The interaction of intense femtosecond laser pulses with wide band-gap fused silica and quartz is investigated. It is shown that during target irradiation, melting of SiO2 occurs. Laser pulses with fluences above the damage threshold induce partial phase transition of fused silicia into quartz and vice-versa.

BACKGROUND: Randomized clinical trials have shown the 9-valent human papillomavirus (HPV) vaccine to be highly effective against types 31/33/45/52/58 compared with the 4-valent. Evidence on the added health and economic benefit of the 9-valent is required for policy decisions. We compare population-level effectiveness and cost-effectiveness of 9- and 4-valent HPV vaccination in the United States. METHODS: We used a multitype individual-based transmission-dynamic model of HPV infection and disease (anogenital warts and cervical, anogenital, and oropharyngeal cancers), 3% discount rate, and societal perspective. The model was calibrated to sexual behavior and epidemiologic data from the United States. In our base-case, we assumed 95% vaccine-type efficacy, lifelong protection, and a cost/dose of $145 and $158 for the 4- and 9-valent vaccine, respectively. Predictions are presented using the mean (80% uncertainty interval [UI] = 10(th)−90(th) percentiles) of simulations. RESULTS: Under base-case assumptions, the 4-valent gender-neutral vaccination program is estimated to cost $5500(80% UI = 2400–9400) and $7300 (80% UI = 4300−11 000)/quality-adjusted life-year (QALY) gained with and without cross-protection, respectively. Switching to a 9-valent gender-neutral program is estimated to be cost-saving irrespective of cross-protection assumptions. Finally, the incremental cost/QALY gained of switching to a 9-valent gender-neutral program (vs 9-valent girls/4-valent boys) is estimated to be $140 200 (80% UI = 4200−>1 million) and $31 100 (80% UI = 2100−>1 million) with and without cross-protection, respectively. Results are robust to assumptions about HPV natural history, screening methods, duration of protection, and healthcare costs. CONCLUSIONS: Switching to a 9-valent gender-neutral HPV vaccination program is likely to be cost-saving if the additional cost/dose of the 9-valent is less than $13. Giving females the 9-valent vaccine provides the majority of benefits of a gender-neutral strategy.

Objective To investigate the incremental cost effectiveness of two dose human papillomavirus vaccination and of additionally giving a third dose. Design Cost effectiveness study based on a transmission dynamic model of human papillomavirus vaccination. Two dose schedules for bivalent or quadrivalent human papillomavirus vaccines were assumed to provide 10, 20, or 30 years’ vaccine type protection and cross protection or lifelong vaccine type protection without cross protection. Three dose schedules were assumed to give lifelong vaccine type and cross protection. Setting United Kingdom. Population Males and females aged 12-74 years. Interventions No, two, or three doses of human papillomavirus vaccine given routinely to 12 year old girls, with an initial catch-up campaign to 18 years. Main outcome measure Costs (from the healthcare provider’s perspective), health related utilities, and incremental cost effectiveness ratios. Results Giving at least two doses of vaccine seems to be highly cost effective across the entire range of scenarios considered at the quadrivalent vaccine list price of £86.50 (€109.23; $136.00) per dose. If two doses give only 10 years’ protection but adding a third dose extends this to lifetime protection, then the third dose also seems to be cost effective at £86.50 per dose (median incremental cost effectiveness ratio £17 000, interquartile range £11 700-£25 800). If two doses protect for more than 20 years, then the third dose will have to be priced substantially lower (median threshold price £31, interquartile range £28-£35) to be cost effective. Results are similar for a bivalent vaccine priced at £80.50 per dose and when the same scenarios are explored by parameterising a Canadian model (HPV-ADVISE) with economic data from the United Kingdom. Conclusions Two dose human papillomavirus vaccine schedules are likely to be the most cost effective option provided protection lasts for at least 20 years. As the precise duration of two dose schedules may not be known for decades, cohorts given two doses should be closely monitored.

Background Recent evidence suggests that two doses of HPV vaccines may be as protective as three doses in the short-term. We estimated the incremental cost-effectiveness of two- and three-dose schedules of girls-only and girls & boys HPV vaccination programmes in Canada. Methods We used HPV-ADVISE, an individual-based transmission-dynamic model of multi-type HPV infection and diseases (anogenital warts, and cancers of the cervix, vulva, vagina, anus, penis and oropharynx). We conducted the analysis from the health payer perspective, with a 70-year time horizon and 3% discount rate, and performed extensive sensitivity analyses, including duration of vaccine protection and vaccine cost. Findings Assuming 80% coverage and a vaccine cost per dose of $85, two-dose girls-only vaccination (vs. no vaccination) produced cost/quality-adjusted life-year (QALY)-gained varying between $7900–24,300. The incremental cost-effectiveness ratio of giving the third dose to girls (vs. two doses) was below $40,000/QALY-gained when: (i) three doses provide longer protection than two doses and (ii) two-dose protection was shorter than 30 years. Vaccinating boys (with two or three doses) was not cost-effective (vs. girls-only vaccination) under most scenarios investigated. Interpretation Two-dose HPV vaccination is likely to be cost-effective if its duration of protection is at least 10 years. A third dose of HPV vaccine is unlikely to be cost-effective if two-dose duration of protection is longer than 30 years. Finally, two-dose girls & boys HPV vaccination is unlikely to be cost-effective unless the cost per dose for boys is substantially lower than the cost for girls.

Background Two-dose human papillomavirus (HPV) vaccine schedules may provide short-term protection but their long-term population impact is unknown. Methods Two models of HPV transmission and associated cervical disease (squamous and glandular, neoplasia and cancer) were fitted to data from England and Canada on HPV epidemiology, sexual behaviour, cervical screening outcomes and cervical cancer incidence. Results Models suggest that at 40–80% coverage, if two-dose schedules protect vaccinees for 20 years, then the benefits of the third dose are small. If two doses protect for 10 years, then the third dose may prevent as many cancers as the first two. At 80% coverage, numbers needed to receive a third dose to prevent an additional cancer are 5900–110,000 (England), 3000–5100 (Canada) with 20 years two-dose protection, and 2000–5300 (England), 760–950 (Canada) with 10 years two-dose protection. Conclusion Results enable decision makers to quantify risks associated with two-dose schedules despite remaining uncertainties in vaccine duration and cross-protection.

Randomized clinical trials are currently examining the efficacy of a nonavalent human papillomavirus (HPV) vaccine, including HPV-types 6/11/16/18/31/33/45/52/58. Evidence on the cost-effectiveness of the nonavalent is required for timely policy-decisions. We compared the potential cost-effectiveness of the nonavalent and quadrivalent HPV vaccines. We used a multi-type individual-based transmission-dynamic model of HPV infection and diseases, 70-year time-horizon, 3% discount rate and healthcare payer perspective. We calibrated the model to Canadian sexual behavior and epidemiologic data, and estimated Quality-Adjusted Life-Years (QALYs) lost and costs ($CAN 2010) from the literature. Under base-case assumptions (vaccinating 10-year-old girls, 80% coverage, 95$/dose, vaccine-type efficacy = 95%, cross-protection for the quadrivalent vaccine, duration of vaccine-type protection (cross-protection) = 20 (10) years), using the quadrivalent and nonavalent vaccines is estimated to cost $15,528 [12,056; 19,140] and $12,203 [9,331; 17,292] per QALY-gained, respectively. At equal price, the nonavalent vaccine is more cost-effective than the quadrivalent vaccine, even when assuming both shorter duration of protection (nonavalent = 20 years vs. quadrivalent = lifelong) and lower vaccine-type efficacy (nonavalent = 85% vs. quadrivalent = 95%). However, the additional cost per dose of the nonavalent vaccine should not exceed $11 to remain more cost-effective than the quadrivalent vaccine, and $24 to represent a cost-effective alternative to the quadrivalent vaccine (using a $40,000/QALY-gained threshold). The nonavalent vaccine can be a cost-effective alternative to the quadrivalent vaccine, even in scenarios where nonavalent vaccine efficacy is 85%. However, because most cervical cancers are caused by HPV-16/18, it is unlikely that the nonavalent would be used if its efficacy against these types is lower than current HPV vaccines.

Background: Papanicolaou smear screening has significantly reduced cervical cancer morbidity and mortality. However, inequalities still persist across different socioeconomic status (SES) groups. These inequalities have been associated with differential participation in screening. However, even with equal participation to screening, some women may still have greater risk of cervical cancer because of sexual behavior. We aim to identify the sociodemographic characteristics of women who reported greater sexual activity and/or screening underuse. Methods: We used data from (i) the Canadian Community Health Survey—2005, a population-based survey of 130,000 Canadians, and (ii) a multicenter study including 952 women screened for cervical cancer. Results: Aboriginals and women with lower SES reported greater sexual activity and lower screening participation, which may produce synergetic effects toward higher cervical cancer risk. Women who did not complete high school and aboriginals were, respectively, 3.6 and 2.5 times more likely to report sexual debut before 15 years old compared with women with university degree and Caucasians. Women who did not complete high school were 2.2 times more likely to have never been screened compared with women with university degree. East and South Asian women were, respectively, 4.3 and 3.1 times more likely to have never been screened than Canadian-born women but reported lower levels of sexual activity and were adherent to screening guidelines when screened at least once. Conclusions: The success of human papillomavirus vaccination at reducing cervical cancer and inequalities will depend on achieving high coverage among high-risk subpopulations. Impact: These groups must be monitored closely, and if need be, targeted for additional interventions. Cancer Epidemiol Biomarkers Prev; 22(4); 641–52. ©2013 AACR.

Background The quadrivalent and bivalent human papillomavirus (HPV) vaccines are now licensed in several countries. We compared the cost-effectiveness of the HPV vaccines to provide evidence for policy decisions. Methods We developed HPV-ADVISE, a multi-type individual-based transmission-dynamic model of HPV infection and disease (anogenital warts, and cervical, anogenital and oropharyngeal cancers). We calibrated the model to sexual behavior and epidemiologic data from Canada, and estimated quality-adjusted life-years (QALYs) lost and costs ($CAN 2010) from the literature. Vaccine-type efficacy was based on a systematic literature review. The analysis was performed from the healthcare provider perspective, and costs and benefits were discounted at 3%. Predictions are presented using the median [10th;90th percentiles] of simulations. Results Under base-case assumptions (vaccinating 10-year-old girls, 80% coverage, $95/dose), using the quadrivalent and bivalent vaccines is estimated to cost $15,528 [12,056;19,140] and $20,182 [15,531;25,240] per QALY-gained, respectively. At equal price, the quadrivalent vaccine is more cost-effective than bivalent under all scenarios investigated, except when assuming longer duration of protection for the bivalent and minimal anogenital warts burden. Under base-case assumptions, the maximum additional cost per dose for the quadrivalent vaccine to remain more cost-effective than the bivalent is $32 [17;46] (using a $40,000/QALY-gained threshold). Results were most sensitive to discounting, time-horizon, differences in durations of protection and anogenital warts burden. Conclusions Vaccinating pre-adolescent girls against HPV is predicted to be highly cost-effective. If equally priced, the quadrivalent is the most economically desirable vaccine. However, ultimately, the most cost-effective HPV vaccine will be determined by their relative price.

Background Bivalent and quadrivalent human papillomavirus (HPV) vaccines are now licensed in several countries. Furthermore, clinical trials examining the efficacy of a nonavalent vaccine are underway. We aimed to compare the potential population-level effectiveness of the bivalent, quadrivalent, and candidate nonavalent HPV vaccines. Methods We developed an individual-based, transmission-dynamic model of HPV infection and disease in a population stratified by age, gender, sexual activity, and screening behavior. The model was calibrated to highly stratified sexual behavior, HPV epidemiology, and cervical screening data from Canada. Results Under base case assumptions, vaccinating 12-year-old girls (70% coverage) with the bivalent (quadrivalent) vaccine is predicted to reduce the cumulative incidence of anogenital warts (AGWs) by 0.0% (72.1%), diagnosed cervical intraepithelial neoplasia lesions 2 and 3 (CIN2 and -3) by 51.0% (46.1%), and cervical squamous cell carcinoma (SCC) by 31.9% (30.5%), over 70 years. Changing from a bivalent (quadrivalent) to a nonavalent vaccine is predicted to reduce the cumulative number of AGW episodes by an additional 66.7% (0.0%), CIN2 and -3 episodes by an additional 9.3% (12.5%), and SCC cases by an additional 4.8% (6.6%) over 70 years. Differences in predicted population-level effectiveness between the vaccines were most sensitive to duration of protection and the time horizon of analysis. The vaccines produced similar effectiveness at preventing noncervical HPV-related cancers. Conclusions The bivalent vaccine is expected to be slightly more effective at preventing CIN2 and -3 and SCC in the longer term, whereas the quadrivalent vaccine is expected to substantially reduce AGW cases shortly after the start of vaccination programs. Switching to a nonavalent vaccine has the potential to further reduce precancerous lesions and cervical cancer.

We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons?