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

Coupled Impacts of Soil Acidification and Climate Change on Future Crop Suitability in Ethiopia

Agricultural sustainability faces challenges in the changing climate, particularly for rain-fed systems like those in Ethiopia. This study examines the combined impacts of climate change and soil acidity on future crop potential, focusing on Ethiopia as a case study. The EcoCrop crop suitability model was parameterized and run for four key food crops in Ethiopia (teff, maize, barley and common wheat), under current and mid-century climate conditions. To assess the impacts of soil acidification on crop suitability, a simulation study was conducted by lowering the soil pH values by 0.5, 1.0 and 1.5 and re-running the suitability model, comparing the changes in the area suitable for each crop. Our evaluation of the model, by comparing the modeled suitable areas with reference data, indicated that there was a good fit for all the four crops. Using default soil pH values, we project that there will be no significant changes in the suitability of maize, barley and wheat and an increase in the suitability of teff by the mid-century, as influenced by projected increases in rainfall in the country. Our results demonstrate a direct relationship between the lowering of soil pH and increasing losses in the area suitable for all crops, but especially for teff, barley and wheat. We conclude that soil acidification can have a strong impact on crop suitability in Ethiopia under climate change, and precautionary measures to avoid soil acidification should be a key element in the design of climate change adaptation strategies

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

The effect of single low-dose primaquine treatment for uncomplicated Plasmodium falciparum malaria on haemoglobin levels in Ethiopia: a longitudinal cohort study.

BACKGROUND: To interrupt residual malaria transmission and achieve successful elimination of Plasmodium falciparum in low-transmission settings, the World Health Organization (WHO) recommends the administration of a single dose of 0.25 mg/kg (or 15 mg/kg for adults) primaquine (PQ) combined with artemisinin-based combination therapy (ACT), without glucose-6-phosphate dehydrogenase (G6PD) testing. However, due to the risk of haemolysis in patients with G6PD deficiency (G6PDd), PQ use is uncommon. Thus, this study aimed to assess the safety of a single low dose of PQ administered to patients with G6PD deficiency. METHODS: An observational cohort study was conducted with patients treated for uncomplicated P. falciparum malaria with either single-dose PQ (0.25 mg/kg) (SLD PQ) + ACT or ACT alone. Microscopy-confirmed uncomplicated P. falciparum malaria patients visiting public health facilities in Arjo Didessa, Southwest Ethiopia, were enrolled in the study from September 2019 to November 2022. Patients with uncomplicated P. falciparum malaria were followed up for 28 days through clinical and laboratory diagnosis, such as measurements of G6PD levels and haemoglobin (Hb) concentrations. G6PD levels were measured by a quantiative CareSTART™ POCT S1 biosensor machine. Patient interviews were also conducted, and the type and frequency of clinical complaints were recorded. Hb data were taken on days (D) 7, 14, 21, and 28 following treatment with SLD-PQ + ACT or ACT alone. RESULTS: A total of 249 patients with uncomplicated P. falciparum malaria were enrolled in this study. Of these, 83 (33.3%) patients received ACT alone, and 166 (66.7%) received ACT combined with SLD-PQ treatment. The median age of the patients was 20 (IQR 28-15) years. G6PD deficiency was found in 17 (6.8%) patients, 14 males and 3 females. There were 6 (7.2%) and 11 (6.6%) phenotypic G6PD-deficient patients in the ACT alone and ACT + SLD-PQ arms, respectively. The mean Hb levels in patients treated with ACT + SLD-PQ were reduced by an average of 0.45 g/dl (95% CI = 0.39 to 0.52) in the posttreatment phase (D7) compared to a reduction of 0.30 g/dl (95% CI = 0.14 to - 0.47) in patients treated with ACT alone (P = 0.157). A greater mean Hb reduction was observed on day 7 in the G6PDd ACT + SLD-PQ group (- 0.60 g/dL) than in the G6PDd ACT alone group (- 0.48 g/dL); however, there was no statistically significant difference (P = 0.465). Overall, D14 losses were 0.10 g/dl (95% CI = - 0.00 to 0.20) and 0.05 g/dl (95% CI = - 0.123 to 0.22) in patients with and without SLD-PQ, respectively (P = 0.412). CONCLUSIONS: This studys findings indicate that using SLD-PQ in combination with ACT is safe for uncomplicated P. falciparum malaria regardless of the patients G6PD status in Ethiopian settings. Caution should be taken in extrapolating this finding in other settings with diverse G6DP phenotypes