On optimal fuzzy best proximity coincidence points of fuzzy order preserving proximal Ψ(σ, α)-lower-bounding asymptotically contractive mappings in non-Archimedean fuzzy metric spaces

This paper discusses some convergence properties in fuzzy ordered proximal approaches defined by {(gn,Tn)}­sequences of pairs, where g:A→A is a surjective self-mapping and T:A→B, where Aand Bare nonempty subsets of and abstract nonempty set X and (X,M,∗,≺̲) is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metric M, a triangular norm * and an ordering ≺̲. The fuzzy set M takes values in a sequence or set {Mσn} where the elements of the so-called switching rule {σn}⊂Z+ are defined from X×X×Z0+ to a subset of Z+. Such a switching rule selects a particular realization of M at the nth iteration and it is parameterized by a growth evolution sequence {αn} and a sequence or set {ψσn} which belongs to the so-called Ψ(σ,α)-lower-bounding mappings which are defined from [0, 1] to [0, 1]. Some application examples concerning discrete systems under switching rules and best approximation solvability of algebraic equations are discussed.

High prevalence of HIV infection among injection drug users (IDUs) in Hyderabad and Sukkur, Pakistan.

OBJECTIVE: To estimate size of injection drug users (IDU), determine their high risk behaviours and assess the prevalence of HIV. METHOD: As part of second generation surveillance (SGS), we investigated specific demographic and behavioural characteristics of IDUs in Hyderabad and Sukkur in 2005. It was a cross sectional study. The survey was preceded by geographic mapping to determine size estimation and to define sampling procedures prior to integrated behavioural and biological survey (IBBS). A sample size of at least 400 was calculated for each city. Besides calculating frequencies, chi square was used for comparing variables among HIV positive and negative IDUs like time elapsed as IDU, number of injections, sharing needles and self perception of acquiring HIV infection. RESULTS: A total of 800 (Hyderabad 398; Sukkur 402) questionnaires and DBS samples were collected. The estimated number of IDUs in both cities was 3,225 (Hyderabad 975 and Sukkur 2250 respectively). Average age of IDUs in Hyderabad was 36.5 years and 34.6 years in Sukkur. Sharing of injection equipment for last injection was reported by 34 (8.5%) in Hyderabad and 135 (33.6%) in Sukkur. In both cities behaviours such as injecting drugs for more than 10 years (p = 0.00) and injecting four or more times in a day (p = 0.11) were significantly associated with seropositivity of HIV infection. In Hyderabad the seroprevalence of HIV was 25.4% (101/398) and in Sukkur it was 19.2% (77/402). CONCLUSION: The burden of HIV among IDUs in Hyderabad and Sukkur is extremely high and can play a significant role in transmitting the infection to other vulnerable groups.

Risky sexual behavior, knowledge of sexually transmitted infections and treatment utilization among a vulnerable population in Rawalpindi, Pakistan.

As a part of a second generation surveillance, we investigated the sociodemographics, risky sexual behavior, knowledge of HIV and sexually transmitted infections (STIs) and treatment seeking behavior among a vulnerable population. A cross-sectional study preceded by mapping, was conducted in Rawalpindi, Pakistan during 2005. Subjects were recruited through snowball, time location cluster and cluster sampling techniques. Behavioral interviews were conducted with 203 female sex workers (FSWs), 101 male sex workers (MSWs), 101 Hijras (transgender men) and 200 injecting drug users (IDUs), who were deemed a vulnerable population for STIs. Among this population 136 (67%) FSWs were illiterate, 145 (71.4%) were married and entertained on average 23 clients per month. Consistent condom use during one month was reported by 34 (17%) FSWs. One hundred thirty-three (66%) FSWs had a knowledge of STIs, 69 (34%) suffered from STIs. MSWs and Hijras had the youngest average ages at 24.4 (+/- 6.8), 25.8 (+/- 5.9) and started sexual activity even at age 14.7, and 13.9 years, respectively. Consistent condom usage was as low as 3 (3.1%) and 4 (4%) among MSWs and Hijras. IDUs had lowest monthly income of US$ 69 (+/- 41) and had a predominant migratory pattern. Fifty (25.2%) IDUs shared a needle with the last injection. Though knowledge of STIs was lowest among IDUs, 61 (30.7%), however, all utilized the public health facility for their treatment. Difference between knowledge of STIs and educational levels among IDUs and Hijras were found to be statistically significant (p=0.015 and p=0.04, respectively). The present study indicates the knowledge of HIV/STIs is high among the vulnerable population but condom usage is very low.