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In this paper it is shown that the question of the existence of a classical solution of the first initial-boundary value problem for a non-linear parabolic equation may be reduced to the problem of the derivation of suitable a priori bounds.
The effectiveness of influenza vaccination programmes is seldom known during an epidemic. We developed an internet-based system to record influenza-like symptoms and response to infection in a participating cohort. Using self-reports of influenza-like symptoms and of influenza vaccine history and uptake, we estimated vaccine effectiveness (VE) without the need for individuals to seek healthcare. We found that vaccination with the 2010 seasonal influenza vaccine was significantly protective against influenza-like illness (ILI) during the 2010–2011 influenza season (VE 52%, 95% CI 27–68). VE for individuals who received both the 2010 seasonal and 2009 pandemic influenza vaccines was 59% (95% CI 27–77), slightly higher than VE for those vaccinated in 2010 alone (VE 46%, 95% CI 9–68). Vaccinated individuals with ILI reported taking less time off work than unvaccinated individuals with ILI (3·4 days vs. 5·3 days, P<0·001).
High titres of pertussis toxin (PT) antibody have been shown to be predictive of recent infection with Bordetella pertussis. The seroprevalence of standardized anti-PT antibody was determined in six Western European countries between 1994 and 1998 and related to historical surveillance and vaccine programme data. Standardized anti-PT titres were calculated for a series of whole-cell and acellular pertussis vaccine trials. For the serological surveys, high-titre sera (>125 units/ml) were distributed throughout all age groups in both high- (>90%) and low-coverage (<90%) countries. High-titre sera were more likely in infants in countries using high-titre-producing vaccines in their primary programme (Italy, 11·5%; Western Germany, 13·3%; France, 4·3%; Eastern Germany, 4·0%) compared to other countries (The Netherlands, 0·5%; Finland, 0%). Recent infection was significantly more likely in adolescents (10–19 years old) and adults in high-coverage countries (Finland, The Netherlands, France, East Germany), whereas infection was more likely in children (3–9 years old) than adolescents in low-coverage (<90%; Italy, West Germany, United Kingdom) countries. The impact and role of programmatic changes introduced after these surveys aimed at protecting infants from severe disease by accelerating the primary schedule or vaccinating older children and adolescents with booster doses can be evaluated with this approach.
Serological surveys among representative population samples have proved rare given their reliance on invasive sample collection. We therefore completed the first population-based postal survey of immunity in England and Wales using new oral fluid technology. This paper examines the feasibility of this new methodological approach. Nearly 5500 oral fluid samples were collected, with individual demographic and social data via a questionnaire, from persons under 45 years of age recruited through general practices. Instructions were accurately followed with only 1% of samples returned without risk-factor data. The overall response rate was 40%. Response was independently associated with age, sex and location. Response was highest in children aged 5–14 years, adult females and in rural locations. This approach allowed the successful collection of comprehensive individual risk data, but response rates in adults must be improved if oral fluid surveys are to routinely complement serological surveillance.
Six countries (Denmark, England and Wales, France, Germany, Italy and the Netherlands) conducted large serological surveys for mumps, in the mid-1990s, as part of the European Sero-Epidemiology Network (ESEN). The assay results were standardized and related to the schedules and coverage of the immunization programmes and the reported incidence of mumps. Low incidence of disease and few susceptibles amongst adolescents and young adults was observed in countries with high mumps vaccine coverage (e.g. the Netherlands). High disease incidence and large proportions of mumps virus antibody negative samples in adolescent and young adult age groups was noted in countries with poor vaccine coverage (e.g. Italy). The build-up of susceptibles in older children and adolescents in England and Wales, France, the former West Germany and Italy indicate the possibility of further mumps outbreaks in secondary school environments. To control mumps in western Europe, current MMR immunization programmes will need to be strengthened in a number of countries. Sero-surveillance of mumps is an important component of disease control and its usefulness will be enhanced by the development of an international mumps standard.
The European Regional Office of WHO has targeted measles for elimination from the region in 2007. Large national, age and sex stratified serological surveys of measles antibody were conducted in seven Western European countries from 1994–8 as part of the European Sero-epidemiology Network. Three patterns were observed in the country-specific measles seroprofiles, ranging from (very) low susceptibility (four countries) to high susceptibility (one country). Susceptibility levels amongst 2–4-year-olds ranged from 2·9 to 29·8 %, in 5–9-year-olds from 2·5 to 25 % and 10–19-year-olds from 2·1 % to 13·9 %. A country's susceptibility profile was highly associated with vaccine coverage for the first dose. First dose coverage ranged from 91 to 97·5 % for low susceptibility countries, 75 to 85 % for intermediate susceptibility countries and 55 % for the high susceptibility country. Only the high susceptibility country still reports epidemic measles. In low susceptibility countries, which have achieved or are very close to measles elimination, the priority will be to maintain high MMR vaccine coverage in all geopolitical units for both vaccine doses. In moderate susceptibility countries there is still some endemic transmission, but also risk of outbreaks as pools of susceptibles accumulate. In the high susceptibility country the priority will be to increase infant vaccine coverage and reduce regional variation in coverage levels.
The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Advances have shed light upon classical problems in this area, and this book presents a fresh approach, largely based upon the results of the authors. The emphasis here is on a topic of central importance in analysis, namely the relationship between i) function spaces on Euclidean n-space and on domains; ii) entropy numbers in quasi-Banach spaces; and iii) the distribution of the eigenvalues of degenerate elliptic (pseudo) differential operators. The treatment is largely self-contained and accessible to non-specialists. Both experts and newcomers alike will welcome this unique exposition.