A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

High HIV incidence and prevalence among young women in rural South Africa: Developing a cohort for intervention trials

Objective: To measure prevalence and model incidence of HIV infection. Setting: 2013 consecutive pregnant women attending public sector antenatal clinics in 1997 in Hlabisa health district, South Africa. Historical seroprevalence data, 1992-1995. Methods: Serum remaining from syphilis testing was tested anonymously for antibodies to HIV to determine seroprevalence. Two models, allowing for differential mortality between HIV-positive and HIV-negative people, were used. The first used serial seroprevalence data to estimate trends in annual incidence. The second, a maximum likelihood model, took account of changing force of infection and age-dependent risk of infection, to estimate age-specific HIV incidence in 1997. Multiple logistic regression provided adjusted odds ratios (OR) for risk factors for prevalent HIV infection. Results: Estimated annual HIV incidence increased from 4% in 1992/1993 to 10% in 1996/1997. In 1997, highest age-specific incidence was 16% among women aged between 20 and 24 years. in 1997, overall prevalence was 26% (95% confidence interval [CI], 24%-28%) and at 34% was highest among women aged between 20 and 24 years. Young age (<30 years; odds ratio [OR], 2.1; p = .001), unmarried status (OR 2.2; p = .001) and living in less remote parts of the district (OR 1.5; p = .002) were associated with HIV prevalence in univariate analysis. Associations were less strong in multivariate analysis. Partner's migration status was not associated with HIV infection. Substantial heterogeneity of HIV prevalence by clinic was observed (range 17%-31%; test for trend, p = .001). Conclusions: This community is experiencing an explosive HIV epidemic. Young, single women in the more developed parts of the district would form an appropriate cohort to test, and benefit from, interventions such as vaginal microbicides and HIV vaccines.

Estimating HIV incidence rates from age prevalence data in epidemic situations

We present a method of estimating HIV incidence rates in epidemic situations from data on age-specific prevalence and changes in the overall prevalence over time. The method is applied to women attending antenatal clinics in Hlabisa, a rural district of KwaZulu/Natal, South Africa, where transmission of HIV is overwhelmingly through heterosexual contact. A model which gives age-specific prevalence rates in the presence of a progressing epidemic is fitted to prevalence data for 1998 using maximum likelihood methods and used to derive the age-specific incidence. Error estimates are obtained using a Monte Carlo procedure. Although the method is quite general some simplifying assumptions are made concerning the form of the risk function and sensitivity analyses are performed to explore the importance of these assumptions. The analysis shows that in 1998 the annual incidence of infection per susceptible woman increased from 5.4 per cent (3.3-8.5 per cent; here and elsewhere ranges give 95 per cent confidence limits) at age 15 years to 24.5 per cent (20.6-29.1 per cent) at age 22 years and declined to 1.3 per cent (0.5-2.9 per cent) at age 50 years; standardized to a uniform age distribution, the overall incidence per susceptible woman aged 15 to 59 was 11.4 per cent (10.0-13.1 per cent); per women in the population it was 8.4 per cent (7.3-9.5 per cent). Standardized to the age distribution of the female population the average incidence per woman was 9.6 per cent (8.4-11.0 per cent); standardized to the age distribution of women attending antenatal clinics, it was 11.3 per cent (9.8-13.3 per cent). The estimated incidence depends on the values used for the epidemic growth rate and the AIDS related mortality. To ensure that, for this population, errors in these two parameters change the age specific estimates of the annual incidence by less than the standard deviation of the estimates of the age specific incidence, the AIDS related mortality should be known to within +/-50 per cent and the epidemic growth rate to within +/-25 per cent, both of which conditions are met. In the absence of cohort studies to measure the incidence of HIV infection directly, useful estimates of the age-specific incidence can be obtained from cross-sectional, age-specific prevalence data and repeat cross-sectional data on the overall prevalence of HIV infection. Several assumptions were made because of the lack of data but sensitivity analyses show that they are unlikely to affect the overall estimates significantly. These estimates are important in assessing the magnitude of the public health problem, for designing vaccine trials and for evaluating the impact of interventions. Copyright (C) 2001 John Wiley & Sons, Ltd.

An epidemic of violence?: Changing patterns in reported rapes in Victoria

Victoria Police statistics show that, since the late 1980s, there has been a significant increase in reported rapes in that State. One interpretation of this trend is that there has been an increase in the underlying incidence of sexual violence in the community. An alternative explanation is that rape victims have become more willing to report to the police, in response to factors such as improved provision of support services to sexual assault victims, reforms to substantive and procedural law, and changes in police attitudes and procedures. In order to rest these competing interpretations data were collected and analysed on the characteristics of rapes reported to the Victoria Police in the late 1980s/early 1990s. This analysis showed that: (I) most of the additional offences reported in the early 1990s were allegations of rapes committed by family members, spouses and other intimates; and (2) an increasing number of reports related to offences which had been committed at feast one year prior to a report being made to the police. It is argued that these changing patterns are consistent with a significant increase in the reporting rate for rape. More generally, the research reported in this paper highlights the limitations of reported crime statistics as measures of the level of social violence, and points to the need for crime researchers to develop alternative methodologies for measuring and interpreting trends.

Multiple impacts of the HIV/AIDS epidemic on the aged in rural Uganda

This paper reports research conducted among theaged residents of a rural, Southwestern Ugandanvillage. It documents their knowledge ofHIV/AIDS, their perceptions of their own riskof infection, and the multiple impacts of thecurrent HIV/AIDS epidemic on their lives. Mostolder individuals have a sound understanding ofthe sexual transmission of HIV, and someconsider themselves to be at risk of infectionthrough having multiple sexual partners. Theyattempt to limit their children's exposure toHIV, but many of these children have left thevillage to live in urban areas of relativelyhigh HIV prevalence. The loss of adult childrendeprives the aged of any support these childrenmight have provided as their parents'capabilities declined with advancing age.Female-headed households were more affected inthis way than were male-headed households. TheAIDS epidemic has increased the number ofburials taking place in the village, and theiraccumulated costs, both in time and money, andcreated new hardships for the aged, who alsohave to cope with grief that accompaniescontinuing deaths among their children andtheir contemporaries' children.

Chloroquine or sulfadoxine-pyrimethamine for the treatment of uncomplicated, Plasmodium falciparum malaria during an epidemic in Central Java, Indonesia

A recent malaria epidemic in the Menoreh Hills of Central Java has increased concern about the re-emergence of endemic malaria on Java, which threatens the island's 120 million residents. A 28-day, in-vivo test of the efficacy of treatment of malaria with antimalarial drugs was conducted among 16 7 villagers in the Menoreh Hills. The treatments investigated, chloroquine (CQ) and sulfadoxine pyrimethamine (SP), constitute, respectively, the first- and second-line treatments for uncomplicated malaria in Indonesia. The prevalence of malaria among 1389 residents screened prior to enrollment was 33%. Treatment outcomes were assessed by microscopical diagnoses, PCR-based confirmation of the diagnoses, measurement of the whole-blood concentrations of CQ and desethylchloroquine (DCQ), and identification of the Plasmodium falciparum genotypes. The 28-day cumulative incidences of therapeutic failure for CQ and SP were, respectively, 47% (N = 36) and 22% (N = 50) in the treatment of P. falciparum, and 18% (N = 77) and 67% (N = 6) in the treatment of P. vivax. Chloroquine was thus an ineffective therapy for P. falciparum malaria, and the presence of CQ-resistant P. vivax and SP-resistant P. falciparum will further compromise efforts to control resurgent malaria on Java.

Winter intervention against Aedes aegypti (Diptera : Culicidae) larvae in subterranean habitats slows surface recolonization in summer

At semiarid Charters Towers, north Queensland, Australia, the importance of Aedes aegypti (L.) in wells was assessed in relation to the colonization of surface habitats during the wet season. From April to July 1999, 10 wells (five positive for Ae. aegypti) were monitored to assess their status and larvae population numbers therein. All surface containers located within a 100 m radius of each well were removed, treated with s-methoprene or sealed to prevent the utilization of these containers by mosquitoes. These inner cores were surrounded by outer zones for a further 100 m in which surface containers were left untreated but all subterranean habitats were treated. Ovitraps were monitored monthly in the inner cores for 36 wk from August 1999 to April 2000 and differences in the proportions of ovitraps positive for Ae. aegypti and Ochlerotatus notoscriptus (Skuse) were analyzed by logistic regression. Analysis of the proportions of ovitraps positive for Ae. aegypti near positive wells indicated significantly greater colonization from November to March (the wet season), compared with those situated near Ae. aegypti negative wells. As Oc. notoscriptus were not produced from subterranean sites, comparisons of the proportions of ovitraps positive for Oc. notoscriptus in positive and negative inner cores provided an indication of the relative productivity of the uncontrolled surface containers in the outer zones. Differences in the utililization of ovitraps by Oc. notoscriptus among positive and negative cores were observed during only one month (March), when oviposition was greater in ovitraps in the negative cores, compared with the positive cores. Best subsets linear regression analysis of the proportion of ovitraps positive for Ae. aegypti against meteorological variables (rainfall, mean wind speed, mean relative humidity, mean minimum, and maximum temperature) during the week of ovitrapping indicated that minimum temperature and wind speed accounted for 63.4% of the variability. This study confirms that for semiarid towns such as Charters Towers, the practice of treating a relatively small number of key subterranean habitats during winter will significantly affect Ae. aegypti recolonization of surface container habitats during summer, the period of greatest risk for dengue.

Sitting time and work patterns as indicators of overweight and obesity in Australian adults

BACKGROUND: Increasing levels of physical inactivity and sedentariness are contributing to the current overweight and obesity epidemic. In this paper, the findings of two recent studies are used to explore the relationships between sitting time ( in transport, work and leisure), physical activity and body mass index (BMI) in two contrasting samples of adult Australians. METHODS: Data on sitting time, physical activity, BMI and a number of demographic characteristics were compared for participants in two studies-529 women who were participants in a preschool health promotion project ('mothers'), and 185 men and women who were involved in a workplace pedometer study ('workers'). Relationships between age, number of children, physical activity, sitting time, BMI, gender and work patterns were explored. Logistic regression was used to predict the likelihood of being overweight or obese, among participants with different physical activity, sitting time and work patterns. RESULTS: The total reported time spent sitting per day ( across all domains) was almost 6 h less among the mothers than the workers (P