http://ir.haramaya.edu.et//hru/handle/123456789/220 2026-04-20T12:34:23Z 2026-04-20T12:34:23Z Abduraman Wako Kolbi Seleshi Demie (PhD) Getinet Alemayehu (PhD) http://ir.haramaya.edu.et//hru/handle/123456789/7657 2024-03-13T06:10:57Z 2023-02-01T00:00:00Z

TRANSIENT ANALYSIS OF MULTI-SERVER MARKOVIAN QUEUE UNDER VARIANT WORKING VACATIONS WITH BALKING AND RENEGING Abduraman Wako Kolbi; Seleshi Demie (PhD); Getinet Alemayehu (PhD) In this thesis, the transient analysis of multi-server markovian queue under variant working vacations with balking, waiting servers and reneging was studied. Customers arrive according to Poisson process and decide to join the queue with a probability �� or balk with complementary probability 1−��. The service times during a regular busy period are considered to be an exponential random variable, with the rate of μ. When the busy period is over, the servers waits for a random duration of time before beginning a vacation. After the completion of the servers waiting period, if there is no customer is in the queue, the servers are allowed to take their first working vacations. When the first working vacations period ends, the servers inspects the system and switches to a normal busy period if there are customers in the queue; otherwise, it takes another working vacation and continues to do so until it has taken at most K consecutive working vacations. The reneging property is due to the customer impatience during working vacation period, during which the servers provides service at a slower rate. The service times during the regular busy period, working vacations period, and vacation times are assumed to be exponentially distributed and mutually independent. To formulate the mathematical equations of the model, the forward Kolmogorov differential equation and Markovian continuous properties have been used. We obtained the transient-state probabilities in terms of the modified Bessel function of the first kind by employing probability-generating functions, continued fractions, some properties of hyper-geometric functions, higher-order matrices, and Laplace transform. Which is useful in understanding and optimizing system behaviors such as capture system dynamics which provides insights into how a queueing system evolves over time. We also obtained some performance measures. Numerical illustrations in the form of graphs and tables were presented to show the behavior of the system size probabilities using Matlab2019 software. Finally, this work with heterogeneous servers under the same model will improved in future work. 90

2023-02-01T00:00:00Z Dimie, Dito(MSc) Teshome, Getachew (PhD) Tefera, Melisew (PhD) http://ir.haramaya.edu.et//hru/handle/123456789/4702 2022-02-15T06:02:36Z 2022-01-01T00:00:00Z

MATHEMATICAL MODEL OF CERVICAL CANCER DUE TO HUMAN PAPILLOMAVIRUS DYNAMICS WITH VACCINATION IN CASE OF GAMO ZONE ARBAMINCH ETHIOPIA Dimie, Dito(MSc); Teshome, Getachew (PhD); Tefera, Melisew (PhD) The main purpose of this study was to propose and analyze a nonlinear mathematical model for the transmission dynamics of cervical cancer due to human papillomavirus with vaccination. The aim of this study is to investigate the dynamics of cervical cancer and analyze a deterministic mathematical model for the spread of cervical cancer due to HPV dynamics with vaccination. To conduct the study, a deterministic mathematical model system of ordinary differential equation and numerical simulation were used. The total population (or sample size) of this model is sub-divided in to five compartments, namely; Susceptible (S), Vaccinated (V), Infected (I), permanently Recovered () and temporary Recovered (). Data of the study was collected through document analysis of recorded data and used to estimate the most influential parameters such as infection rate, vaccination rate and recovery rate. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest Eigen value of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibrium are determined. We used Maple 18 software in order to check the effect of some parameters in the expansion as well as in the control of cervical cancer dynamics. From the numerical simulation results we concluded that increasing the recovery rate has a great contribution to eradicate cervical cancer infection in the community and decreasing the contact rate can also have a great contribution to eliminate the cervical cancer. Moreover, our numerical simulation results indicated that increasing vaccination rate and decreasing contact rate is vital to eradicate the cervical cancer disease. 71

2022-01-01T00:00:00Z Budul, Kadar(MSc) Demie, Seleshi (PhD) Tefera, Melisew (PhD) Alemayehu, Getinet (PhD) http://ir.haramaya.edu.et//hru/handle/123456789/4697 2022-02-14T12:09:13Z 2021-06-01T00:00:00Z

DETERMINANTS OF STUDENTS' PERFORMANCE IN MATHEMATICS : THE CASE OF Dr. ABDULMEJID HUSSEIN COLLEGE OF TEACHERS EDUCATION, SOMALI REGIONAL STATE Budul, Kadar(MSc); Demie, Seleshi (PhD); Tefera, Melisew (PhD); Alemayehu, Getinet (PhD) This study was aimed to find out the determinants of students' performance in mathematics at Dr. Abdulmejid Hussein College of Teachers Education. In order to meet this aim attention was given to the Socio-demographic, students, teachers and institution related determinants. The study employed descriptive survey research design and it incorporated both qualitative and quantitative approaches. From a population of 146 second and third year students, 107 samples were selected by using simple random sampling technique. By available sampling, 12 mathematics teachers, 1 mathematics department head and 1 academic dean were included in the study. The data collection tools were questionnaire, observation and document analysis. The quantitative data were analyzed by descriptive statistics such as frequency and percentage with the help of SPSS version 16. The results of the study show that determinants related to students were lack of base in mathematics, lack of study habit, not securing first choice department, lack of academic preparedness to study mathematics. The socio-demographic determinants influenced the students’ performance were the students’ former schools, parents’ educational level and low SES. Also the teachers related determinants that affected students’ performance were the experience and subject specialization of the teachers, teaching methods, assessment and feedback, lack of teachers course preparation. The institutional determinants of students’ performance in mathematics was the institution's low commitment and not establishing mechanisms that can improve the students’ mathematics performance. Lack of facilities and conducive environment both for the students and teachers, Also, the curriculum changed to the Af-somali language which is not given the emphasis it deserves affected the students’ performance in mathematics and created scarcity of resources and manpower. Therefore, it is recommended that, college, department head and mathematics teachers should make more effort to build the base and attitude of the students by giving remedial classes, guidance and counselling, also the students should work hard. Teachers should use active teaching methods, continuous assessments and give feedback the students on time to improve their performance and adjust their study habit. The institution and mathematics department head should create a mechanism that can improve students’ performance in mathematics and pay attention to the admission and department placement of the students, the college and the SRS education bureau should fulfill the facilities needed both for the students and teachers. The institution and mathematics department together need to organize workshops, panel discussions and trainings to update the teachers and share experience with the mathematics departments of the colleges of teachers in the country and promote the shared values to the concerned stakeholders. 79

2021-06-01T00:00:00Z Gebreselassie, Zinabu (MSc) Teshome, Getachew (PhD) Tefera, Melisew (PhD) http://ir.haramaya.edu.et//hru/handle/123456789/4603 2021-11-05T06:18:29Z 2020-12-01T00:00:00Z

STOCHASTIC MODEL OF TUBERCULOSIS WITH VACCINATION OF NEWBORNS IN CASE OF EASTREN ETHIOPIA Gebreselassie, Zinabu (MSc); Teshome, Getachew (PhD); Tefera, Melisew (PhD) In this thesis we formulated a Stochastic Model of Tuberculosis with Vaccination of Newborns for studying the dynamics of Tuberculosis (TB) by incorporating vaccination of newly born babies and the aim of this work is to develop and analyze qualitatively both the stochastic and the deterministic models of the population dynamics of tuberculosis for the purpose of studying the effect of vaccination coverage. The total population in this model is sub-divided in to four compartments, namely Susceptible, Infected, Vaccinated newborns and Recovered. First, the developed model is expressed and analyzed by deterministic approach. Since this approach neglects the randomness of the dynamics of the process, it has limitations in the modeling process. To avoid this kind of issues we transformed the deterministic approach into a stochastic one, which is known to play a significant role by providing additional degree of realism compared to the deterministic approach. The invariant region of the solution, conditions for positivity of the solution, existence of equilibrium points of the model and their stabilities and also sensitivity analysis are checked. Additionally we showed that in both deterministic and stochastic case the effective reproduction number is less than one, then the disease free equilibrium point is stable so that the disease die out. According to the analysis, we came to realize that the basic reproduction number for the stochastic approach is smaller than deterministic one and which shows us stochastic approach is closer to reality than the deterministic one. To conduct the thesis, secondary datas for infected, recovered and vaccinated population were collected from randomly selected Diredawa and Harar Hospitals. We have conducted various numerical experiments to analyze the collectded data using Euler’s method by MATLAB software and obtained interesting simulation results which indicate that combination of increased newborn vaccination has a great contribution in combating TB. It is worth mentioning that the simulation results confirm the conclusion drawn from the qualitative analysis of the model. Hence, we came to realize that the number of infected people keeps decreasing if one carefully combines vaccination with appropriate treatment and decrease the contct between susceptible and infected indeviduals. Therefore, we recommend that a combination of a decrease in contact between infected and susceptible individuals, increasing vaccination coverage, creating awareness to decrease contact rate and increasing recovery rate with proper treatment to effectively control TB infection. 57

2020-12-01T00:00:00Z