Cost-effectiveness analysis of hepatitis E vaccination strategies among patients with chronic hepatitis B in China.

AIM: This study aimed to evaluate the cost-effectiveness of hepatitis E vaccination strategies in chronic hepatitis B (CHB) patients. METHODS: Based on the societal perspective, the cost-effectiveness of three hepatitis E vaccination strategies-vaccination without screening, screening-based vaccination, and no vaccination-among CHB patients was evaluated using a decision tree-Markov model, and incremental cost-effectiveness ratios (ICERs) were calculated. Values for treatment costs and health utilities were estimated from a prior investigation on disease burden, and values for transition probabilities and vaccination-related costs were obtained from previous studies and government agencies. Sensitivity analyses were undertaken for assessing model uncertainties. RESULTS: It was estimated that CHB patients superinfected with hepatitis E virus (HEV) incurred significantly longer disease course, higher economic burden, and more health loss compared to those with HEV infection alone (all p < 0.05). The ICERs of vaccination without screening and screening-based vaccination compared to no vaccination were 41,843.01 yuan/quality-adjusted life year (QALY) and 29,147.32 yuan/QALY, respectively, both lower than China's per-capita gross domestic product (GDP) in 2018. The screening-based vaccination reduced the cost and gained more QALYs than vaccination without screening. One-way sensitivity analyses revealed that vaccine price, vaccine protection rate, and decay rate of vaccine protection had the greatest impact on the cost-effectiveness analysis. Probabilistic sensitivity analyses confirmed the base-case results, and if the willingness-to-pay value reached per-capita GDP, the probability that screening-based vaccination would be cost-effective was approaching 100%. CONCLUSIONS: The disease burden in CHB patients superinfected with HEV is relatively heavy in China, and the screening-based hepatitis E vaccination strategy for CHB patients is the most cost-effective option.

COVID-19 vaccine coverage targets to inform reopening plans in a low incidence setting.

Since the emergence of SARS-CoV-2 in 2019 through to mid-2021, much of the Australian population lived in a COVID-19-free environment. This followed the broadly successful implementation of a strong suppression strategy, including international border closures. With the availability of COVID-19 vaccines in early 2021, the national government sought to transition from a state of minimal incidence and strong suppression activities to one of high vaccine coverage and reduced restrictions but with still-manageable transmission. This transition is articulated in the national 're-opening' plan released in July 2021. Here, we report on the dynamic modelling study that directly informed policies within the national re-opening plan including the identification of priority age groups for vaccination, target vaccine coverage thresholds and the anticipated requirements for continued public health measures-assuming circulation of the Delta SARS-CoV-2 variant. Our findings demonstrated that adult vaccine coverage needed to be at least 60% to minimize public health and clinical impacts following the establishment of community transmission. They also supported the need for continued application of test-trace-isolate-quarantine and social measures during the vaccine roll-out phase and beyond.

Optimal vaccination: various (counter) intuitive examples.

In previous articles, we formalized the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-dimensional metapopulation model. The aim of the current paper is to illustrate this theoretical framework with multiple examples where one can derive the analytic expression of the optimal strategies. We discuss in particular the following points: whether or not it is possible to vaccinate optimally when the vaccine doses are given one at a time (greedy vaccination strategies); the effect of assortativity (that is, the tendency to have more contacts with similar individuals) on the shape of optimal vaccination strategies; the particular case where everybody has the same number of neighbors.

Effective Vaccination and Education Strategies for Emerging Infectious Diseases Such as COVID-19.

Social isolation and control owing to coronavirus disease 2019 (COVID-19) are easing; however, concerns regarding new infectious diseases have not disappeared. Given epidemic experiences such as severe acute respiratory syndrome (SARS), the influenza pandemic, Middle East respiratory syndrome (MERS), and COVID-19, it is necessary to prepare for the outbreak of new infectious diseases and situations in which large-scale vaccinations are required. Although the development of vaccines against COVID-19 has contributed greatly to overcoming the pandemic, concerning vaccine side effects from the general public, including medical personnel, and decreased confidence in vaccine efficacy and side effects, present many challenges in promoting and educating vaccinations for new infectious diseases in the future. In addition to plans to develop vaccines for the outbreak of new infectious diseases, education and promotion plans are necessary to administer the latest developments of vaccines to the general public. Moreover, efforts are needed to secure the necessity, legitimacy, and evidence for rapid vaccination on a large scale at the national level. It is also necessary to carefully prepare scientific bases and explanatory statements so that the general public can easily understand them. This study aimed to establish vaccine strategies and vaccination education plans for new infectious diseases that may occur in the future. Many ways to promote vaccination to the general public and healthcare workers should be prepared to ensure that the latest vaccines against new infectious diseases are administered safely. Thus, education and promotion of vaccine efficacy and safety based on specific data from clinical studies are necessary.

Exploring epidemic voluntary vaccinating behavior based on information-driven decisions and benefit-cost analysis.

A complex dynamic interplay exists between epidemic transmission and vaccination, which is significantly influenced by human behavioral responses. We construct a research framework combining both the function modeling of the cumulative global COVID-19 information and limited individuals' information processing capacity employing the Gompertz model for growing processes. Meanwhile, we built a function representing the decision to get vaccinated following benefit-cost analysis considered the choices made by people in each scenario have an influence from altruism, free-riding and immunity escaping capacity. Through the mean-field calculation analysis and using a fourth-order Runge-Kutta method with constant step size, we obtain plots from numerical simulations. We found that only when the total number of infectious individuals proves sufficient to reach and exceed a certain level will the individuals face a better trade-off in determining whether to get vaccinated against the diseases based on that information. Besides, authoritative media have a higher decisive influence and efforts should be focused on extending the duration of vaccine protection, which is beneficial to inhibit the outbreaks of epidemics. Our work elucidates that reducing the negative payoff brought about by the free-riding behavior for individuals or improving the positive payoff from the altruistic motivation helps to control the disease in cultures that value social benefits, vaccination willingness is generally stronger. We also note that at a high risk of infection, the decision of vaccination is highly correlated with global epidemic information concerning COVID-19 infection, while at times of lower risk, it depends on the game theoretic vaccine strategy. The findings demonstrate that improving health literacy, ensuring open and transparent information on vaccine safety and efficacy as a public health priority can be an effective strategy for mitigating inequalities in health education, as well as alleviating the phenomenon that immunity escaping abilities is more likely to panic by populations with high levels of education. In addition, prosocial nudges are great ways to bridge these immunity gaps that can contribute to implementing government public health control measures, creating a positive feedback loop.

A two-sex model of human papillomavirus infection: Vaccination strategies and a case study.

Vaccination is effective in preventing human papillomavirus (HPV) infection. It still remains debatable whether males should be included in a vaccination program and unclear how to allocate the vaccine in genders to achieve the maximum benefits. In this paper, we use a two-sex model to assess HPV vaccination strategies and use the data from Guangxi Province in China as a case study. Both mathematical analysis and numerical simulations show that the basic reproduction number, an important indicator of the transmission potential of the infection, achieves its minimum when the priority of vaccination is given to the gender with a smaller recruit rate. Given a fixed amount of vaccine, splitting the vaccine evenly usually leads to a larger basic reproduction number and a higher prevalence of infection. Vaccination becomes less effective in reducing the infection once the vaccine amount exceeds the smaller recruit rate of the two genders. In the case study, we estimate the basic reproduction number is 1.0333 for HPV 16/18 in people aged 15-55. The minimal bivalent HPV vaccine needed for the disease prevalence to be below 0.05% is 24050 per year, which should be given to females. However, with this vaccination strategy it would require a very long time and a large amount of vaccine to achieve the goal. In contrast with allocating the same vaccine amount every year, we find that a variable vaccination strategy with more vaccine given in the beginning followed by less vaccine in later years can save time and total vaccine amount. The variable vaccination strategy illustrated in this study can help to better distribute the vaccine to reduce the HPV prevalence. Although this work is for HPV infection and the case study is for a province in China, the model, analysis and conclusions may be applicable to other sexually transmitted diseases in other regions or countries.

Health technology assessment to employ COVID-19 serological tests as companion diagnostics in the vaccination campaign against SARS-CoV-2.

OBJECTIVES: In scenarios of vaccine scarcity or contexts of organizational complexity, it is necessary to define prioritization strategies for allocating vaccine doses in compliance with the criterion of equity and efficiency of health resources. In this context, the COVIDIAGNOSTIX project, based on the health technology assessment (HTA), assessed the role of SARS-CoV-2 serological tests as a companion diagnostic in the definition of the vaccination strategies for the vaccine administration. To guarantee evidence support for health policy choices, two different vaccine strategies were analyzed, one based on administering the vaccine booster dose to the entire population (VACCINE strategy) and the other based on allocation criteria (TEST&VACCINE strategy). METHODS: The decision-oriented HTA (DoHTA) method, integrated with specific modeling and simulation techniques, helped define the perimeter to make health policy choices. RESULTS: The processing of the scores attributed to the key performance indicators concerning all the evaluation domains shows a performance of 94.34% for the TEST&VACCINE strategy and 83.87% for the VACCINE strategy. CONCLUSIONS: TEST&VACCINE strategy can be the most advantageous in various scenarios due to greater speed from an operational and an economic point of view. The assessment schemes defined by COVIDIAGNOSTIX (i.e., technologies/intended use/settings) can easily and quickly be exported and adapted to respond to similar health "policy questions".

Assessing Age-Specific Vaccination Strategies and Post-vaccination Reopening Policies for COVID-19 Control Using SEIR Modeling Approach.

As the availability of COVID-19 vaccines, it is badly needed to develop vaccination guidelines to prioritize the vaccination delivery in order to effectively stop COVID-19 epidemic and minimize the loss. We evaluated the effect of age-specific vaccination strategies on the number of infections and deaths using an SEIR model, considering the age structure and social contact patterns for different age groups for each of different countries. In general, the vaccination priority should be given to those younger people who are active in social contacts to minimize the number of infections, while the vaccination priority should be given to the elderly to minimize the number of deaths. But this principle may not always apply when the interaction of age structure and age-specific social contact patterns is complicated. Partially reopening schools, workplaces or households, the vaccination priority may need to be adjusted accordingly. Prematurely reopening social contacts could initiate a new outbreak or even a new pandemic out of control if the vaccination rate and the detection rate are not high enough. Our result suggests that it requires at least nine months of vaccination (with a high vaccination rate > 0.1%) for Italy and India before fully reopening social contacts in order to avoid a new pandemic.

The impact of vaccination on human papillomavirus infection with disassortative geographical mixing: a two-patch modeling study.

Human papillomavirus (HPV) infection can spread between regions. What is the impact of disassortative geographical mixing on the dynamics of HPV transmission? Vaccination is effective in preventing HPV infection. How to allocate HPV vaccines between genders within each region and between regions to reduce the total infection? Here we develop a two-patch two-sex model to address these questions. The control reproduction number [Formula: see text] under vaccination is obtained and shown to provide a critical threshold for disease elimination. Both analytical and numerical results reveal that disassortative geographical mixing does not affect [Formula: see text] and only has a minor impact on the disease prevalence in the total population given the vaccine uptake proportional to the population size for each gender in the two patches. When the vaccine uptake is not proportional to the population size, sexual mixing between the two patches can reduce [Formula: see text] and mitigate the consequence of disproportionate vaccine coverage. Using parameters calibrated from the data of a case study, we find that if the two patches have the same or similar sex ratios, allocating vaccines proportionally according to the new recruits in two patches and giving priority to the gender with a smaller recruit rate within each patch will bring the maximum benefit in reducing the total prevalence. We also show that a time-variable vaccination strategy between the two patches can further reduce the disease prevalence. This study provides some quantitative information that may help to develop vaccine distribution strategies in multiple regions with disassortative mixing.

Effect of population heterogeneity on herd immunity and on vaccination decision making process.

We study the influence of population heterogeneity on herd immunity level and on individual's vaccination decision making process. We first formulate the mathematical model in a population with two subgroups, based on different activity levels or different susceptibilities. The herd immunity threshold is derived and discussed. It is calculated that the required vaccine coverage level for herd immunity in a heterogeneous mixing population can be varied significantly. The required vaccine coverage level is lower than the classical herd immunity level, if the vaccine coverage level in the more active group or more susceptible group is higher than the other subgroup. It is suggested that the classical herd immunity levels can be misleading in the process of planning mass vaccination programs. The analysis is further extended to study the population with more subgroups. We then study the formal vaccination games to simulate the process of vaccination decision making, in either homogeneous or heterogeneous mixing populations. It is proved that the Nash equilibrium in the vaccination game is not unique if population heterogeneity is considered. Moreover, herd immunity is not achieved if individuals are solely driven by self-interests.

Assessing intervention strategies for non-homogeneous populations using a closed form formula for R0.

A general stochastic model for susceptible → infective → recovered (SIR) epidemics in non-homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex models. The basic reproduction number R0, an indication of the probability of an outbreak for homogeneous populations does not indicate the probability of an outbreak for non-homogeneous models anymore, because it changes with the initially infected case. Therefore, we use "individual R0" that is the expected number of secondary cases for a unique given initially infected individual. Thus, the effectiveness of intervention strategies can be assessed by their capability to reduce individual R0 values. Also a vaccination plan based on individual R0 values for fully heterogeneous populations is proposed. It is based on the recursive calculation of individual R0 values.

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.

Uncertainty quantification of a mathematical model of COVID-19 transmission dynamics with mass vaccination strategy.

In this paper, the uncertainty quantification and sensitivity analysis of a mathematical model of the SARS-CoV-2 virus transmission dynamics with mass vaccination strategy has been carried out. More specifically, a compartmental epidemic model has been considered, in which vaccination, social distance measures, and testing of susceptible individuals have been included. Since the application of these mitigation measures entails a degree of uncertainty, the effects of the uncertainty about the application of social distance actions and testing of susceptible individuals on the disease transmission have been quantified, under the assumption of a mass vaccination program deployment. A spectral approach has been employed, which allows the uncertainty propagation through the epidemic model to be represented by means of the polynomial chaos expansion of the output random variables. In particular, a statistical moment-based polynomial chaos expansion has been implemented, which provides a surrogate model for the compartments of the epidemic model, and allows the statistics, the probability distributions of the interesting output variables of the model at a given time instant to be estimated and the sensitivity analysis to be conducted. The purpose of the sensitivity analysis is to understand which uncertain parameters have most influence on a given output random variable of the model at a given time instant. Several numerical experiments have been conducted whose results show that the proposed spectral approach to uncertainty quantification and sensitivity analysis of epidemic models provides a useful tool to control and mitigate the effects of the COVID-19 pandemic, when it comes to healthcare resource planning.

Epidemic Dynamics and Adaptive Vaccination Strategy: Renewal Equation Approach.

We use analytical methods to investigate a continuous vaccination strategy's effects on the infectious disease dynamics in a closed population and a demographically open population. The methodology and key assumptions are based on Breda et al. (J Biol Dyn 6(Sup2):103-117, 2012). We show that the cumulative force of infection for the closed population and the endemic force of infection in the demographically open population can be reduced significantly by combining two factors: the vaccine effectiveness and the vaccination rate. The impact of these factors on the force of infection can transform an endemic steady state into a disease-free state.

Estimating the fiscal impact of three vaccination strategies in Italy.

OBJECTIVES: When assessing the economic value of vaccines, decision makers should adopt a full societal perspective. One approach for estimation of the fiscal impact of a disease is to use the human capital method to determine productivity losses. The aim of this study was to test an analytical framework developed for the estimation of the fiscal impacts of vaccination programs for influenza (FLU), pneumococcus (PC), and herpes zoster (HZ), in Italy. METHODS: We tested the framework in a two-stage analysis. First, we estimated the fiscal impact of the disease, second we performed a cost-benefit analysis of the individual benefits of vaccination against the cost of the vaccine. To estimate the fiscal impact of the diseases, the human capital approach was used. Epidemiological data were extrapolated from the literature. A Monte Carlo simulation enabled exploration of the uncertainty in the model variables. RESULTS: For FLU, assuming 2.1 million people infected, the total expected impact was EUR 999,371,520; the estimated fiscal impact was EUR 159,563,520. For PC, assuming 90,000 people infected, the total impact was EUR 148,055,040 and the estimated fiscal impact was EUR 23,639,040. For HZ, assuming 6,400 people infected, the total impact was EUR 4,777,200, with EUR 630,000 resulting from a decrease in fiscal taxation. CONCLUSIONS: In conclusion, our work shows how traditional methods aimed at estimating the cost of illness from a social perspective can be improved by additionally considering the fiscal impact, which accounts for the decrease in fiscal revenues due to illness.

Evaluating the potential impact of targeted vaccination strategies against severe acute respiratory syndrome coronavirus (SARS-CoV) and Middle East respiratory syndrome coronavirus (MERS-CoV) outbreaks in the healthcare setting.

BACKGROUND: Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS) are two coronaviruses with demonstrated potential to generate significant nosocomial outbreaks. In particular, MERS continues to pose a significant threat in the Middle East since 2012. Currently, no licensed vaccine or drug treatment is available to treat patients infected with either coronavirus. However, there are some MERS vaccines in the preclinical stage of development. We sought to evaluate the potential impact of targeted vaccination strategies for mitigating SARS and MERS outbreaks in healthcare settings using simple mathematical models and detailed historic transmission trees describing the progression of past nosocomial outbreaks of SARS and MERS. RESULTS: Our findings suggest that vaccination strategies targeting patients and healthcare workers, which have been disproportionately affected during past outbreaks, and assuming two vaccination coverage levels at 50 and 75% have the potential to avert nearly 50% or more of MERS or SARS cases. CONCLUSION: Our modeling results informed by historic outbreak data for SARS and MERS suggest that vaccination strategies targeting patients could be an effective measure to mitigate and prevent outbreaks in the healthcare setting.

A systematic review of BCG vaccination policies among high-risk groups in low TB-burden countries: implications for vaccination strategy in Canadian indigenous communities.

BACKGROUND: Bacille Calmette-Guérin (BCG) vaccination against tuberculosis (TB) is widespread in high-TB-burden countries, however, BCG vaccination policies in low-burden countries vary. Considering the uncertainties surrounding BCG efficacy and the lower likelihood of TB exposure in low-incidence countries, most have discontinued mass vaccination, choosing instead a targeted vaccination strategy among high-risk groups. Given the increased risk of TB infection in Canadian Indigenous communities compared to the general Canadian population, these communities are a pertinent example of high-incidence groups in an otherwise low-burden country, warranting particular consideration regarding BCG vaccination strategy. This systematic review aims to synthesise and critically appraise the literature on BCG vaccination strategies in high-risk groups in low-incidence settings to provide policy considerations relevant to the Canadian Indigenous context. METHODS: A literature search of the Medline and Embase databases was conducted, returning studies pertaining to BCG vaccine efficacy, TB incidence under specific vaccination policies, BCG-associated adverse events, and vaccination policy guidelines in low-burden countries. Study screening was tracked using the Covidence systematic review software (Veritas Health Innovation, Melbourne, Australia), and data pertaining to the above points of interest were extracted. RESULTS: The final review included 49 studies, spanning 15 countries. Although almost all of these countries had implemented a form of mass or routine vaccination previously, 11 have since moved to targeted vaccination of selected risk groups, in most cases due to the low risk of infection among the general population and thus the high number of vaccinations needed to prevent one case in the context of low-incidence settings. Regarding identifying risk groups for targeted screening, community-based (rather than individual risk-factor-based) vaccination has been found to be beneficial in high-incidence communities within low-incidence countries, suggesting this approach may be beneficial in the Canadian Indigenous setting. CONCLUSIONS: Community-based vaccination of high-incidence communities may be beneficial in the Canadian Indigenous context, however, where BCG vaccination is implemented, delivery strategies and potential barriers to achieving adequate coverage in this setting should be considered. Where an existing vaccination program is discontinued, it is crucial that an effective TB surveillance system is in place, and that case-finding, screening, and diagnostic efforts are strengthened in order to ensure adequate TB control. This is particularly relevant in Canadian Indigenous and other remote or under-served communities, where barriers to surveillance, screening, and diagnosis persist.

Incidence of hepatitis B virus infection in young Chinese blood donors born after mandatory implementation of neonatal hepatitis B vaccination nationwide.

This study was carried out to determine the incidence of hepatitis B virus (HBV) infection in the young generation born after mandatory implementation of hepatitis B vaccination since 1992. Repeat blood donors born between 1992 and 1997 were enrolled, who gave blood at least twice during the past 3 years. Donors were tested for HBV infection markers of HBsAg, anti-HBc, anti-HBs and viral DNA by immunoassays (EIAs) and nucleic acid tests (NAT). A total of 14 937 pre-donation screening qualified young repeat donors aged 18-23 years were tested with 9 (0.06%) being HBsAg by EIA and 10 (1:1494) HBV DNA positive by Ultrio NAT (10.4 IU/mL), respectively. HBV DNA was further detected in 1:192 (9/1732) anti-HBc+ repeat donors with Ultrio Plus NAT (3.4 IU/mL). Most cases were identified as occult HBV infection (OBI). Of 14 937 repeat donors, 20.9% were anti-HBc+ positive, while approximately 50% of 12 024 repeat donors were anti-HBs negative or had levels <100 IU/L. HBsAg+ or OBI strains were classified as wild type of genotype B or genotype C. Incident HBV infection in repeat donors was approximately 1:18.5 person-years (1.1%/year) but significantly less frequent in donors with confirmed HBV vaccination (2.4%-3.3%) than those unsure of vaccination status (10.5%; P = .0023). Hepatitis B virus vaccination appears largely protective of HBV infection, but incidence of infections increases in young adults with mostly undetectable or low anti-HBs or occasionally high anti-HBs. A boost of hepatitis B vaccine for adolescents prior to age 18 years may reduce HBV infection, and implementation of more sensitive NAT in blood donation screening may improve HBV safety in blood transfusion.

Constrained minimization problems for the reproduction number in meta-population models.

The basic reproduction number ([Formula: see text]) can be considerably higher in an SIR model with heterogeneous mixing compared to that from a corresponding model with homogeneous mixing. For example, in the case of measles, mumps and rubella in San Diego, CA, Glasser et al. (Lancet Infect Dis 16(5):599-605, 2016. https://doi.org/10.1016/S1473-3099(16)00004-9 ), reported an increase of 70% in [Formula: see text] when heterogeneity was accounted for. Meta-population models with simple heterogeneous mixing functions, e.g., proportionate mixing, have been employed to identify optimal vaccination strategies using an approach based on the gradient of the effective reproduction number ([Formula: see text]), which consists of partial derivatives of [Formula: see text] with respect to the proportions immune [Formula: see text] in sub-groups i (Feng et al. in J Theor Biol 386:177-187, 2015.  https://doi.org/10.1016/j.jtbi.2015.09.006 ; Math Biosci 287:93-104, 2017.  https://doi.org/10.1016/j.mbs.2016.09.013 ). These papers consider cases in which an optimal vaccination strategy exists. However, in general, the optimal solution identified using the gradient may not be feasible for some parameter values (i.e., vaccination coverages outside the unit interval). In this paper, we derive the analytic conditions under which the optimal solution is feasible. Explicit expressions for the optimal solutions in the case of [Formula: see text] sub-populations are obtained, and the bounds for optimal solutions are derived for [Formula: see text] sub-populations. This is done for general mixing functions and examples of proportionate and preferential mixing are presented. Of special significance is the result that for general mixing schemes, both [Formula: see text] and [Formula: see text] are bounded below and above by their corresponding expressions when mixing is proportionate and isolated, respectively.

Lack of immunity against rubella among Italian young adults.

BACKGROUND: To support the evaluation of the 2010-15 National Plan for Measles and Congenital Rubella Elimination, the authors designed and performed a serosurveillance survey to verify the immunity/susceptibility rate against rubella among Apulian young adults. METHODS: The study was carried out from May 2011 to June 2012 in the Department of Transfusion Medicine/Blood Bank of Policlinico General Hospital in Bari. Subjects were enrolled by a convenience sampling. For each enrolled patient a 5 ml serum sample was collected and tested for anti-rubella IgG. The geometrical means (GMT) of anti-rubella IgG was calculated. T student test or ANOVA test, when appropriate, was used to compare the means of age per gender and GMT of anti-rubella IgG titres per age classes. Chi-square test was used to compare the proportion of anti-rubella IgG positive subjects per gender and per age classes. For all tests, a p value <0.05 was considered as significant. RESULTS: At the end of the study 1764 subjects were enrolled, 1362 (77.2%) of which were male. The mean age was 38.4 ± 11.7 years (range: 17-65). 86.7% (95% CI = 85.0-88.2) had a positive titre of anti-rubella IgG. GMT of anti-rubella IgG titre was 4.3. The proportion of positive subjects was of 76.8% (n = 279/363; 95% CI = 72.2-81.1) in persons aged 18-26 years; 88.1% (n = 310/352; 95% CI = 84.2-91.3) in 27-35 year-old people; 88.5% (n = 464/524; 95% CI = 85.5-91.1) in 36-45 year-old people; 90.7% (n = 350/386; 95% CI = 87.3-93.4) among people aged 46-55 years and 90.6% (n = 126/139; 95% CI = 84.5-94.9) in 55-65 year-old people (Chi-square = 39.7; p < 0.0001). GMT of anti-rubella IgG titre was 4.3 (4.3 in male and 4.2 in female, t = 2.2; p = 0.03) and seems to differ dividing the enrolled subjects by age group (F = 14.3; p < 0.0001). CONCLUSIONS: According to our data, too many women of child-bearing age are still unprotected from rubella in the elimination era and in this scenario the public health efforts should be oriented to catch-up activities.