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.

A two-dimensional fuzzy random model of soil pore structure

A new conceptual model for soil pore-solid structure is formalized. Soil pore-solid structure is proposed to comprise spatially abutting elements each with a value which is its membership to the fuzzy set ''pore,'' termed porosity. These values have a range between zero (all solid) and unity (all pore). Images are used to represent structures in which the elements are pixels and the value of each is a porosity. Two-dimensional random fields are generated by allocating each pixel a porosity by independently sampling a statistical distribution. These random fields are reorganized into other pore-solid structural types by selecting parent points which have a specified local region of influence. Pixels of larger or smaller porosity are aggregated about the parent points and within the region of interest by controlled swapping of pixels in the image. This creates local regions of homogeneity within the random field. This is similar to the process known as simulated annealing. The resulting structures are characterized using one-and two-dimensional variograms and functions describing their connectivity. A variety of examples of structures created by the model is presented and compared. Extension to three dimensions presents no theoretical difficulties and is currently under development.

A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

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.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

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.

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.