College of Natural and Computational Sciences

MATHEMATICAL MODELLING OF CHIKUNGUNYA DISEASE DYNAMICS

Sat, 01 Nov 2025 00:00:00 GMT

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

Comparisons of Influences of Mass Densities of Fuel Briquettes Produced from Eucalyptus, Olive Tree, Sorghum Stalk and Khat Waste Raw Materials On Burning Times

Wed, 01 Jan 2025 00:00:00 GMT

Comparisons of Influences of Mass Densities of Fuel Briquettes Produced from Eucalyptus, Olive Tree, Sorghum Stalk and Khat Waste Raw Materials On Burning Times Kassahun, Wondwosen Global energy demand is rising, causing overexploitation of fossil fuels and environmental challenges. Renewable sources, especially biomass briquettes from residues, offer sustainable alternatives. Ethiopia relies heavily on unsustainable biomass, leading to deforestation and degradation. The rising demand for household energy in Ethiopia has intensified reliance on fuelwood and charcoal, contributing to deforestation and environmental degradation. This study investigates the potential of four locally available biomass raw materials Eucalyptus, Olive tree, Sorghum stalk, and Khat waste—for briquette production. Raw materials (20 kg each) were chopped, air-dried, and carbonized under limited oxygen to produce char powder. The resulting char was mixed with 10% clay binder and water, molded into cylindrical briquettes, and oven-dried. Performance tests were conducted using the water boiling method, measuring density, burning temperature, and effective cooking times. Results revealed significant differences in density and effective cooking time among the briquette types. Khat and Olive tree briquettes exhibited higher densities (0.442 and 0.476 g/cm³) and sustained heating, maintaining water temperatures above 75°C for 101 and 73 minutes, respectively. Sorghum briquettes showed the highest peak temperature (96°C) but had short endurance (40 minutes), while Eucalyptus briquettes demonstrated the lowest density and inconsistent burning behavior, averaging only 31 minutes above 75°C. ANOVA confirmed significant differences (p < 0.05) among treatments, indicating that raw material type strongly influences briquette performance. The findings suggest that Khat waste and Olive tree residues are the most promising biomass feed stocks for producing efficient and sustainable fuel briquettes in Ethiopia, offering a renewable alternative to fuel wood and charcoal while addressing waste management and deforestation concerns. 28

Comparisons of Influences of Mass Densities of Fuel Briquettes Produced from Eucalyptus, Olive Tree, Sorghum Stalk and Khat Waste Raw Materials On Burning Times

Wed, 01 Jan 2025 00:00:00 GMT

Comparisons of Influences of Mass Densities of Fuel Briquettes Produced from Eucalyptus, Olive Tree, Sorghum Stalk and Khat Waste Raw Materials On Burning Times Amente (Prof), Gelana; Mengistu (PhD), Birhanu; KASSAHUN, WONDWOSEN Global energy demand is rising, causing overexploitation of fossil fuels and environmental challenges. Renewable sources, especially biomass briquettes from residues, offer sustainable alternatives. Ethiopia relies heavily on unsustainable biomass, leading to deforestation and degradation. The rising demand for household energy in Ethiopia has intensified reliance on fuelwood and charcoal, contributing to deforestation and environmental degradation. This study investigates the potential of four locally available biomass raw materials Eucalyptus, Olive tree, Sorghum stalk, and Khat waste—for briquette production. Raw materials (20 kg each) were chopped, air-dried, and carbonized under limited oxygen to produce char powder. The resulting char was mixed with 10% clay binder and water, molded into cylindrical briquettes, and oven-dried. Performance tests were conducted using the water boiling method, measuring density, burning temperature, and effective cooking times. Results revealed significant differences in density and effective cooking time among the briquette types. Khat and Olive tree briquettes exhibited higher densities (0.442 and 0.476 g/cm³) and sustained heating, maintaining water temperatures above 75°C for 101 and 73 minutes, respectively. Sorghum briquettes showed the highest peak temperature (96°C) but had short endurance (40 minutes), while Eucalyptus briquettes demonstrated the lowest density and inconsistent burning behavior, averaging only 31 minutes above 75°C. ANOVA confirmed significant differences (p < 0.05) among treatments, indicating that raw material type strongly influences briquette performance. The findings suggest that Khat waste and Olive tree residues are the most promising biomass feed stocks for producing efficient and sustainable fuel briquettes in Ethiopia, offering a renewable alternative to fuel wood and charcoal while addressing waste management and deforestation concerns. 42

A FLUID QUEUE DRIVEN BY SINGLE SERVER MARKOVIAN QUEUE WITH VARIANT WORKING VACATIONS

Wed, 01 Jan 2025 00:00:00 GMT

A FLUID QUEUE DRIVEN BY SINGLE SERVER MARKOVIAN QUEUE WITH VARIANT WORKING VACATIONS LAMORE ADE, TSEGAYE; Demie (PhD), Seleshi; t Alemayehu (PhD), Getine In this thesis a fluid queue driven by single server Markovian queue with variant working vacation was investigated. Queuing theory is a mathematical approach that studies and models waiting lines. A fluid Queue is an input output system the customers are modeled as a continuous fluid that enters and leaves a storage device, called Buffer, Where the background process is governed by a single server Markovian queue. Fluid queues are powerfully applied across diverse fields to model systems where a continuous workload accumulates and depletes under rates controlled by a random environment, typically a Markov chain. In telecommunications, they model data buffers in routers and wireless networks with fluctuating traffic and channel capacity. In manufacturing, they represent continuous-flow production lines subject to machine breakdowns, while in finance, they analyze cash reserves in insurance and dam-based company models. The study focuses on formulating governing equations for background process model and fluid model, the closed-form solutions for steady state probabilities of the system were obtained by applying probability generating functions methods. Various performance measures of the system such as buffer content distribution, mean buffer content, server utilization were obtained. The model captures the dynamics of the system under working vacation polices, where the server operates at a reduced rate rather than being completely idle. Numerical computations were performed by MATLAB software to validate the theoretical results and analyze the system performance under various parameter settings. The findings provide insights into the behavior of fluid queues influenced by Markovian driven vacation polices, contributing to the broader understanding of queuing systems with server vacations. 47