http://ir.haramaya.edu.et//hru/handle/123456789/220 Mon, 22 Jun 2026 10:34:18 GMT 2026-06-22T10:34:18Z http://ir.haramaya.edu.et//hru/handle/123456789/8676 MATHEMATICAL MODELLING OF CHIKUNGUNYA DISEASE DYNAMICS GETACHEW, FETENE In this thesis, we have adapted and modified the existing SEIR-SI Mathematical model by adjusting the vertical transmission in humans, where infected mothers pass the disease to newborns, and introducing insecticide spraying targeting the mosquito population to describe the transmission dynamics of Chikungunya disease. Mathematical analysis of the model yields the basic reproduction number, a key biological threshold parameter that determines disease persistence or elimination was calculated using the next-generation matrix method. The local stability of the disease free equilibrium and the endemic equilibrium was discussed using the Routh-Hurwitze criterion. Also, the global stability of both the disease free and the endemic equilibrium were performed using Lasselle’s invariance principle of Lyapunov functions. The results show that; if , then the disease free equilibrium is globally asymptotically stable, which leads to eradication of the disease and the current intervention (spraying) is effective. Conversely, if , then the endemic equilibrium becomes globally stable, which indicate that the persistence of the disease within the community and stronger intervention are required to bring below one. Sensitivity analysis highlights that the spraying insecticide rate has a significant negative impact on reproduction number, suggest that intensify vector control measures can effectively reduce disease transmission. Meanwhile, the vertical transmission rate has a moderate effect on increasing transmission. Numerical simulation was conducted using MATLAB software to confirm our analytic result 93 Sat, 01 Nov 2025 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/8676 2025-11-01T00:00:00Z http://ir.haramaya.edu.et//hru/handle/123456789/7657 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 Wed, 01 Feb 2023 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/7657 2023-02-01T00:00:00Z http://ir.haramaya.edu.et//hru/handle/123456789/4702 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 Sat, 01 Jan 2022 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/4702 2022-01-01T00:00:00Z http://ir.haramaya.edu.et//hru/handle/123456789/4697 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 Tue, 01 Jun 2021 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/4697 2021-06-01T00:00:00Z