http://ir.haramaya.edu.et//hru/handle/123456789/117 2026-04-17T16:26:58Z 2026-04-17T16:26:58Z Bizuayehu Seyoum Zalale (PhD) Getachew Teshome (PhD) Melisew Tesfera http://ir.haramaya.edu.et//hru/handle/123456789/8384 2025-05-07T07:18:16Z 2024-12-01T00:00:00Z

MODELING AND ANALYZING DIARRHEAL DISEASE DYNAMICS USING CONTROL MEASURES Bizuayehu Seyoum Zalale; (PhD) Getachew Teshome; (PhD) Melisew Tesfera In this study, a mathematical model to analyze the dynamics of a chronic water-borne disease known as diarrhea is developed. To achieve the objectives of this study work, secondary data on the population under five years of age from Bishoftu General Hospital between 2020 and March 2024 is collected. These populations were categorized as newborn, vaccinated, infected, and treated. Based on the epidemiological behavior of the diarrhea disease, a deterministic model is formulated by dividing the total population into seven classes. This model accounts for preventive interventions through vaccination and control measures through treatment. Since diarrhea is caused by pathogens that can survive and reproduce in water at specific temperatures and salinities, so we considered the pathogens as a compartment in the model. Our findings revealed that this water-borne disease can lead to serious infections. The qualitative behavior of the models, including the existence of equilibrium points, basic reproductive number of the model, and stability analysis of equilibrium points were analyzed. Using the collected data, some parameters value were estimated while value some others parameters were received from related publications, and based on the behavior of these disease the values left parameters where assumed. To determine the effect of parameters on the dynamics of the disease, a numerical simulation was performed and displayed the results in a graph using MATLAB 2019 computer software. The results show that increasing the rate of vaccination and treatment plays a crucial role in controlling the dynamics of diarrhea. Therefore, in order to eliminate diarrhea in the community, it is essential for stakeholders to consider these prevention strategies and control measures 62p.

2024-12-01T00:00:00Z MURAD MUMMEDIMER Dr, Seleshi Demie (PhD) Dr. Melisew Tefera (PhD) http://ir.haramaya.edu.et//hru/handle/123456789/8309 2025-03-14T06:11:49Z 2024-06-01T00:00:00Z

MULTI SERVER MARKOVIAN QUEUE WITH MULTIPLE WORKING VACATIONS, WAITING SERVER, FEEDBACK, RENEGING AND RETENTION OF RENEGED CUSTOMERS MURAD MUMMEDIMER; Dr, Seleshi Demie (PhD); Dr. Melisew Tefera (PhD) In this thesis an infinite capacity Multi server Markovian queuing system with multiple working vacations, waiting server, feedback, reneging and retention of reneged customers is examined. If all active servers finish service and these is no customer in the system, the server wait for a duration of time before begin a synchronous WV (waiting server). During WV after completion of each service, customer can either leave the system satisfactorily with probability β or rejoin the queue to get service with feedback com plementary probability 1− β, where 0 ≤ β ≤ 1. The servers serve the customers at a slower rate than the normal busy period during a working vacation and this becomes the cause of customer’s impatience and this impatient customers may remain in the system with probability by employing certain convincing mechanisms. The inter-arrival times, the waiting server times, the feedback times, the service times, the impatient times and the vacation times are taken to be independent and exponentially distributed. The steady state probabilities when the server is in a regular busy period and in a working vacation periods are obtained by using recursive and probability generating function approach, also the steady state probabilities of the system being in any particular state were ob tained by using probability generating function. Various performance measures of the model such as the expected system size during normal busy periods, the expected system size during working vacations periods, the expected system size, the expected number of customer served, the proportion of customers served and the average of reneging and retention rate are obtained by using probability generating function approach. At the end, we have presented some numerical examples to demonstrate the effects of system parameters on some performance measures. 61

2024-06-01T00:00:00Z Tajudin Shafi (PhD) Melisew Tefera (PhD) Getachow Teshome http://ir.haramaya.edu.et//hru/handle/123456789/8290 2025-03-07T12:25:04Z 2024-10-01T00:00:00Z

A METHOD BASED ON BERNSTEIN POLYNOMIAL FOR SOLVING NONLINEAR VOLOTERRA-FREDHOLM INTEGRAL EQUATIONS OF SECOND Tajudin Shafi; (PhD) Melisew Tefera; (PhD) Getachow Teshome In this thesis, we discussed numerical solutions of nonlinear Volterra-Fredholm integral equations by using Bernstein polynomial collocation method. Nonlinear Volterra-Fredholm integral equations which cannot be easily evaluated analytically. This thesis was concerned with numerical method (Bernstein polynomial collocation method). Bernstein polynomial collocation method were utilized to convert the Nonlinear Volterra-Fredholm integral equation into a system of nonlinear algebraic equations and the resulting nonlinear algebraic equations were solved by using newton iteration technique to compute the Bernstein coefficients. The presented concept and method was verified by different examples, where theoretical results are numerically confirmed. The numerical results of six test problems, for which the exact solutions are known, are considered to verify the accuracy and the efficiency of the proposed method. The numerical results were compared with the exact solutions and with other method used for solving nonlinear VFIE based on absolute error. Finally the numerical results were demonstrated by table, in order to show the reliability of proposed method. From the results of the study as the values of the degree n, increases and the error were decreasing and computational costs were increases to obtain more accurate results. Lastly from the result, we have seen that BPCM is converge to exact solution as number of degree is increased. This thesis can be extended to solve nonlinear volterra-fredholm integro differential equation and also can be extended for the numerical solutions of two dimensional nonlinear volterra-fredholm equations using these methods. 74p.

2024-10-01T00:00:00Z sherif Abrahim Esa (PhD) Seleshi Demie (PhD) Getinet Alemayehu http://ir.haramaya.edu.et//hru/handle/123456789/8289 2025-03-07T06:42:21Z 2024-09-01T00:00:00Z

SINGLE SERVER BATCH SERVICE MARKOVIAN(M/M(a,b)/1)QUEUE WITH VARIANT WORKING VACATION sherif Abrahim Esa; (PhD) Seleshi Demie; (PhD) Getinet Alemayehu This research investigates a single server batch service queuing system with Poisson arrivals, exponential service times and a server that takes variant working vacations. During working vacation, the server continues to serve a customer at a reduced rate. The system’s steady state behavior is analyzed using a Markov chain approach. Mathematical equations governing the system’s dynamics are derived, considering the server’s different states: idle, busy, on vacation, and serving during vacations. The inter-arrival times, service times and the duration of working vacation period are taken to be mutually independent and exponentially distributed. Steady state probabilities are obtained by solving linear equations (forward shift operator). Based on these probabilities, we calculate the average of queue length. Finally, numerical illustrations in the form of tables and graphs were presented using MATLAB to show how various parameters of the model influence the behavior of the system. The research findings demonstrate that the variant working vacation policy can significantly influence the system performance. The specific effect depend on the relative magnitudes of the arrival, service, and vacation rates. 53p.

2024-09-01T00:00:00Z