A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems

We define linear programming problems involving trapezoidal fuzzy numbers (LPTra) as the way of linear programming problems involving interval numbers (LPIn). We will discuss the solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers (LPTra) by converting them into two linear programming problems involving interval numbers (LPIn). By introducing new arithmetic operations between interval numbers and fuzzy numbers, we will check that both primal and dual problems have optimal solutions and the two optimal values are equal. Also, both optimal solutions obey the strong duality theorem and complementary slackness theorem. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable

Gonorrhea, Chlamydia and HIV incidence among female sex workers in Cotonou, Benin: A longitudinal study

<div><p>Female sex workers (FSWs) continue to carry a heavy burden of sexually transmitted infections (STI). For prevention purposes, there is a need to identify most-at-risk subgroups among them. The objective of this longitudinal cohort study conducted at <i>Dispensaire IST</i>, Cotonou, Benin, was to assess <i>Neisseria gonorrhoeae</i> (NG) / <i>Chlamydia trachomatis</i> (CT) incidence and determinants; and HIV incidence among FSWs in presence of STI/HIV risk reduction activities. Overall, 319 adult FSWs were followed quarterly from September 2008 to March 2012. NG/CT were detected from endocervical swabs by Amplified DNA Assays employing Strand displacement amplification technology. HIV testing was done on capillary blood using two consecutive rapid diagnostic tests. Anderson-Gill proportional hazard models (HR) were used to determine factors independently associated with NG/CT incidence. The majority of FSWs were HIV-negative (188, 58.9%). There were 6 HIV seroconversions among these 188 HIV-negative women. HIV incidence (95% Confidence interval, CI) was 1.41 (0.28–2.54) seroconversions per 100 person-years at risk (PYAR): 6 events / 425.1 PYAR. Sixty-two out of 319 women experienced 83 new episodes of NG/CT for an overall incidence rate (95% CI) of 10.8 (8.17–13.88) events / 100 PYAR. From month-24 onwards, HIV-positive women (treated: HR (95%CI): 4.2 (1.60–10.77); untreated: HR (95%CI): 4.2 (1.59–11.49) were more likely to acquire NG/CT compared to HIV-negative FSWs. Longer duration in sex work (>2 years: HR; 95%CI: 0.4 (0.22–0.72)) was protective against NG/CT. Refusal by clients (55.8%) was the main reason for non-condom use. Enrolling women from one clinic (<i>Dispensaire IST</i>) may have impaired generalizability of the findings. New NG/CT/HIV infections were observed among FSWs notwithstanding ongoing prevention interventions. To eliminate HIV transmission among FSWs, STI/HIV control programs need to promote women’s empowerment and address vulnerability to infection of HIV-positive FSWs.</p></div

Abolishing Fees at Health Centers in the Context of Community Case Management of Malaria: What Effects on Treatment-Seeking Practices for Febrile Children in Rural Burkina Faso?

Burkina Faso started nationwide community case management of malaria (CCMm) in 2010. In 2011, health center user fees for children under five were abolished in some districts.To assess the effects of concurrent implementation of CCMm and user fees abolition on treatment-seeking practices for febrile children.This is a natural experiment conducted in the districts of Kaya (CCMm plus user fees abolition) and Zorgho (CCMm only). Registry data from 2005 to 2014 on visits for malaria were collected from all eight rural health centers in the study area. Annual household surveys were administered during malaria transmission season in 2011 and 2012 in 1,035 randomly selected rural households. Interrupted time series models were fitted for registry data and Fine and Gray's competing risks models for survey data.User fees abolition in Kaya significantly increased health center use by eligible children with malaria (incidence rate ratio for intercept change = 2.1, p <0.001). In 2011, in Kaya, likelihood of health center use for febrile children was three times higher and CHW use three times lower when caregivers knew services were free. Among the 421 children with fever in 2012, the delay before visiting a health center was significantly shorter in Kaya than in Zorgho (1.46 versus 1.79 days, p <0.05). Likelihood of visiting a health center on the first day of fever among households <2.5 km or <5 km from a health center was two and three times higher in Kaya than in Zorgho, respectively (p <0.001).User fees abolition reduced visit delay for febrile children living close to health centers. It also increased demand for and use of health center for children with malaria. Concurrently, demand for CHWs' services diminished. User fees abolition and CCMm should be coordinated to maximize prompt access to treatment in rural areas

Baseline characteristics of 319 female sex workers, Cotonou, Benin, 2008–2012.

<p>Baseline characteristics of 319 female sex workers, Cotonou, Benin, 2008–2012.</p

Variation in crude NG/CT incidence rates in a cohort of 319 female sex workers, in Cotonou, Benin, 2008–2012.

<p>Variation in crude NG/CT incidence rates in a cohort of 319 female sex workers, in Cotonou, Benin, 2008–2012.</p

Treatment-seeking practices for febrile children according to the caregivers’ knowledge about the abolition of user fees (Kaya, 2011).

<p>Treatment-seeking practices for febrile children according to the caregivers’ knowledge about the abolition of user fees (Kaya, 2011).</p

Prevalence of larval control practices undertaken by mothers in the 2,004 households surveyed.

<p>Notes: In bold, p<0.05 (differences between households’ locations);</p><p>^†Rural high exposure, rural areas with large streams, lakes and/or stagnant water reservoirs</p><p>Prevalence of larval control practices undertaken by mothers in the 2,004 households surveyed.</p

Predicted probabilities of treatment-seeking practices for febrile children (Kaya, 2011).

<p>Notes:</p><p>CI: confidence interval</p><p>HC: health center</p><p>*p <0.05</p><p>***p <0.001</p><p>^¶Multinomial model adjusted for household-level variables (SES, distance to HC), individual-level variables (sex, duration of fever, severity signs, slept under a bednet) and family clustering.</p><p>Predicted probabilities of treatment-seeking practices for febrile children (Kaya, 2011).</p