Eighth order Predictor-Corrector Method to Solve Quadratic Riccati Differential Equations

In this paper, the eighth-order predictor-corrector method is presented for solving quadratic Riccati differential equations. First, the interval is discretized and then the method is formulated by using Newton’s backward difference interpolation formula. The stability and convergence of the method have been investigated. To validate the applicability of the proposed method, two model examples with exact solutions have been considered and numerically solved. Maximum absolute errors are presented in tables and figures for different values of mesh size h and the present method gives better results than some existing numerical methods reported in the literature. &nbsp

Willingness to join a village-based health insurance scheme (Iddir) in Dessie town, Ethiopia

AbstractIntroduction: The total health spending in Ethiopia (both public and private) is still limited and compromises purchase of desired healthcare. There has recently been an increase in interest in health insurance as a promising approach to healthcare financing reform in Ethiopia. Iddirs (indigenous community self-help institutions) appear to have good management practices and are successful in mobilizing communities. This study aimed to estimate the prevalence of the willingness of people in Dessie town, Northeast Ethiopia, to join an iddir-based health insurance scheme, and to identify factors associated with this prevalence.Methods: A cross-sectional study was conducted from February to March 2016 in Dessie town; 636 participants were recruited during that period. Multi-stage sampling was used to select informants and data were collected using face-to-face interviews. Both bivariable and multivariable logistic regressions were used to model the odds of willingness to participate in iddirs.Results: The proportion of people who were willing to join an Iiddir-based health insurance scheme was 83.2%. In terms of willingness to join the health insurance scheme, the odds were likely to be significantly higher among those who attended at least primary school education (AOR = 4.91; 95% CI: 2.21-10.8), those who were wealthy (AOR = 3.39; 95% CI: 1.74-6.58), and those whose family size was greater or equal to five (AOR = 3.42; 95% CI: 2.44-5.15). Being single decreases the willingness to join Iddir-based health Insurance scheme (AOR = 0.29; 95% CI: 0.14-0.55).Conclusion: Iddir association initiated health insurance scheme and considered the possible alternative source of finance for healthcare. The prevalence of willingness to join an iddir-based health insurance scheme was high. Thus, it is recommended to align insurance strategies with the scope of iddirs in order to mobilize the community for sustainable resources generation as an alternative source of finance for healthcare.  [Ethiop. J. Health Dev. 2018;32(4):249-256]Key words: Health insurance, Iddir, Insurance, Dessie, Ethiopi

Enhancing Students’ Attitude towards Mathematics the Case of Three Mettu Secondary and Preparatory Schools in Illu Aba Bora Zone

Students’ success in mathematics depends upon their attitude towards mathematics. It also influences the participation rate and achievement of students. The objective of this research study was to enhance attitude of Mettu Secondary and Preparatory Schools students’ towards mathematics.  A closed ended, self-reported statements questionnaire with Likert type was used to collect data from the concerned stakeholders. Multiple regressions were used for data analysis

Deriving Formulas for Three Integers Such That the Sum of Their Squares and the Sum of Products of Their Squares are Both Perfect Square Integers

In this research study we will derive formulas for three integers whose squares sum and the sum of their squares products are both perfect square integers. That is if and  are three integers, then   and  are both perfect square integers. Proofs are most often arrived at through deductive reasoning. A proof is an argument where a given statement is true. In this proof the so called direct proof had used

Research Based Mathematics Problem Solving and Proving skills Competences

Research findings indicate that addressing problem solving and proving activities each day in the class would affect the thinking and reasoning skills of the students. We discovered that the students became more adept at mathematics problem solving and proving mathematical statements as they practiced various types of mathematical problems and mathematical statements. We also discovered that students worked more diligently on problems of interest to them. Also, some problems are better solved individually, and some are more geared as a group activity. We also proved that they develop the expected skills competences as they practices solving various mathematics problems and proving various mathematical statements

Spatiotemporal variability of soil moisture over Ethiopia and its teleconnections with remote and local drivers

Soil moisture is one of the essential climate variables with a potential impact on local climate variability. Despite the importance of soil moisture, studies on soil moisture characteristics in Ethiopia are less documented. In this study, the spatiotemporal variability of Ethiopian soil moisture (SM) has been characterized, and its local and remote influential driving factors are investigated. An empirical orthogonal function (EOF) and KMeans clustering algorithm have been employed to classify the large domain into homogeneous zones. Complex maximum covariance analysis (CMCA) is applied to evaluate the covariability between SM and selected local and remote variables such as rainfall (RF), evapotranspiration (ET), and sea surface temperature (SST). Inter-comparison among SM datasets highlight that the FLDAS dataset better depicts the country’s SM spatial and temporal distribution (i.e., a correlation coefficient r=0.95 , rmsd=0.04m3m−3 with observations). Results also indicate that regions located in northeastern Ethiopia are drier irrespective of the season (JJAS, MAM, and OND) considered. In contrast, the western part of the country consistently depicted a wetter condition in all seasons. During summer (JJAS), the soil moisture variability is characterized by a strong east–west spatial contrast. The highest and lowest soil moisture values were observed across the country’s central western and eastern parts, respectively. Furthermore, analyses indicate that interannual variability of SM is dictated substantially by RF, though the impact on some regions is weaker. It is also found that ET likely drives the SM in the eastern part of Ethiopia due to a higher atmospheric moisture demand that ultimately invokes changes in surface humidity and rainfall. A composite analysis based on the extreme five wettest and driest SM years revealed a similar spatial distribution of wet SM with positive anomalies of RF across the country and ET over the southern regions. Remote SSTs are also found to have a significant influence on SM distribution. In particular, equatorial central Pacific and western Indian oceans SST anomalies are predominant factors for spatiotemporal SM variations over the country. Major global oceanic indices: Oceanic Nino Index (ONI), Indian Ocean Dipole (IOD), Pacific warm pool (PACWARMPOOL), and Pacific Decadal Oscillations (PDO) are found to be closely associated with the SM anomalies in various parts of the country. The associationship between these remote SST anomalies and local soil moisture is via large-scale atmospheric circulations that are linked to regional factors such as precipitation and temperature anomalies.publishedVersio

Constraints of Students’ Mathematical Problem Solving and Proving Skill Competences, the Case of Four preparatory Schools in Guraghe Zone

The objective of this research study was to assess the constraints in the students’ mathematical problem solving and proving skill competences and propose solutions in order to overcome these problems (or the constraints). A mixed design (quantitative and qualitative designs) approach was used to collect data from the concerned stakeholders involved in the teaching and learning of mathematics. The study was carried out at four preparatory schools in four Woredas of Guraghe zone. Purposive sampling approach was used to select the sample Woredas and preparatory schools and simple random sampling approach was used to select sample section and sample students. As a result, 293 students were taken (70 students   were from Yaberus Secondary and preparatory school, 62 students were from Emdibir, 72 students were from Butajera and 89 students were from Abafiransua secondary and preparatory school). Questionnaires were administered to these students in order to collect the data for the study.Results of the research showed that some of the constraints identified were students’ poor potential: to identify and use appropriate mathematical problem solving and proving strategies and mathematical keywords or indicators, to put connections among mathematical concepts and procedures as well as mathematical ideas with different real world situations, to transform givens in to solutions or required, family and society negative attitudes about mathematics. Moreover, teachers’ method of teaching mathematics and lack of opportunity for using any type of technology (computer program and software) aggravated the problem. It was found that the problems are multifaceted and accordingly the solutions require overall effort from all concerned stakeholders

COVID 19 Epidemic Trajectory Modeling Results for Ethiopia

AbstractBackground: An outbreak of “pneumonia of unknown etiology" later renamed as Novel Corona Virus (COVID 19) was first reported from Hubei Province, China on 31 December 2019. The cases have increased exponentially; the pandemic has reached all countries in the world with 81.2 million confirmed cases and over 1.8 million by December 28, 2020. Ethiopia reported its first case on March 13, 2020, and as of December 28, 2020, the country had 122864 confirmed COVID-19 cases and 1909 deaths. Being a new pandemic its epidemiologic trajectories across regions and populations remains unknown. Mathematical models are widely used to understand and predict the possible courses of an outbreak, given a set of underlying assumptions. Objective: This study intends to model COVID 19 epidemic trajectory under different assumptions and to predict the likely timing of peak of the epidemic in Ethiopia. Methods: Standard Susceptible Exposed, Infected and Recovery (SEIR) compartmental epidemiological deterministic model was employed to estimate and predict COVID 19 in progression in Ethiopia and Addis Ababa at different points of time. Exhaustive literature reviews were carried out to contextualize COVID 19 pandemic epidemiological. Efficacy and coverage of face mask and social distancing were considered in the best and worst situation to run the model and estimate the number of infections after sustained local transmissions. Result. Without any intervention, the COVID 19 viruses spread will peak at 150 days from the first report, infecting 8.01million people given local/community transmission. As the compliance with face mask coverage increases by 25%, 50%, and 75%, the infection will be reduced by about 20%, 40%, and 60% respectively social distancing compliance by le 25% of the population alone will reduce above 60% of infections. Compliance of 40% face mask use and social distance combined effect will reduce 97% of the estimated number of cases. Conclusion: This predication indicated that compliance with combination of non-pharmaceutical intervention such as use of face mask use with physical distance averted significant number of COVID infection. For a county like Ethiopia with poor health systems resilience, mitigating the pandemic at an early stage through strong preventive measures is necessary. [Ethiop. J. Health Dev. 2021; 35(SI-1):25-32] Key word: COVID 19, Modelling, Non-Pharmaceutica intervention, Ethiopi

Genital self-sampling for HPV-based cervical cancer screening: a qualitative study of preferences and barriers in rural Ethiopia

Background In the context of WHO’s “task shifting” project and growing global consensus on primary HPV-based cervical cancer screening, self-sampling is a promising new tool to expand screening access, uptake and coverage for women worldwide. We aimed to explore perceptions and acceptability of HPV self-sampling-based cervical cancer screening among community members and health professionals in rural northwest Ethiopia and to identify preferences and socio-cultural barriers regarding self-sampling in order to design a suitable high-coverage screening intervention for a rural African setting. Methods: Four community-based focus group discussions (FGD) were conducted in the rural district of Dabat, Northwest Ethiopia, each comprising 8 to 14 female participants, counting a total of 41 participants. The groups were homogenously composed in terms of their socio-economic status in the community. They included health centre attendees, community members, nurses and health development army leaders (HDAL). Two qualitative data collection experts conducted the interviews in the local language, using a FGD guide with several thematic areas. All participants granted written informed consent prior to the conduct of the interviews. As a concrete example of an existing self-sampling approach for cervical cancer screening we used the Evalyn® Brush. Results: Emerging themes included (i) misconceptions and low awareness about cervical cancer among community residents and primary health care providers in rural northwest Ethiopia, (ii) stigmatization and social exclusion of affected women, (iii) delay in seeking of health care due to poor access and availability of services, and lacking of a concept of early cancer prevention, (iv) need of spousal permission, (v) fear of financial burden and (vi) fear of social marginalization. The self-sampling device was regarded to be acceptable and was judged to be easy to use for most women. The existing Ethiopian health care structure could facilitate a community approach. Conclusion: Home-based self-sampling for cervical cancer screening is a socially acceptable and feasible “task shifting” method that will increase cervical cancer screening access and coverage in the Ethiopian study community. Education, awareness creation, community mobilization and family inclusion are identified as key activities to promote, implement and facilitate “task shifting” approaches like self-sampling

O-5S quantitative real-time PCR: a new diagnostic tool for laboratory confirmation of human onchocerciasis

Background: Onchocerciasis is a parasitic disease caused by the filarial nematode Onchocerca volvulus. In endemic areas, the diagnosis is commonly confirmed by microscopic examination of skin snip samples, though this technique is considered to have low sensitivity. The available melting-curve based quantitative real-time PCR (qPCR) using degenerated primers targeting the O-150 repeat of O. volvulus was considered insufficient for confirming the individual diagnosis, especially in elimination studies. This study aimed to improve detection of O. volvulus DNA in clinical samples through the development of a highly sensitive qPCR assay. Methods: A novel hydrolysis probe based qPCR assay was designed targeting the specific sequence of the O. volvulus O-5S rRNA gene. A total of 200 clinically suspected onchocerciasis cases were included from Goma district in South-west Ethiopia, from October 2012 through May 2013. Skin snip samples were collected and subjected to microscopy, O-150 qPCR, and the novel O-5S qPCR. Results: Among the 200 individuals, 133 patients tested positive (positivity rate of 66.5%) and 67 negative by O-5S qPCR, 74 tested positive by microscopy (37.0%) and 78 tested positive by O-150 qPCR (39.0%). Among the 133 O-5S qPCR positive individuals, microscopy and O-150 qPCR detected 55.6 and 59.4% patients, respectively, implying a higher sensitivity of O-5S qPCR than microscopy and O-150 qPCR. None of the 67 individuals who tested negative by O-5S qPCR tested positive by microscopy or O-150 qPCR, implying 100% specificity of the newly designed O-5S qPCR assay. Conclusions: The novel O-5S qPCR assay is more sensitive than both microscopic examination and the existing O-150 qPCR for the detection of O. volvulus from skin snip samples. The newly designed assay is an important step towards appropriate individual diagnosis and control of onchocerciasis