Departments of Mathematics
Permanent URI for this collectionhttps://etd.hu.edu.et/handle/123456789/99
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Item MATHEMATICAL MODEL ANALYSIS ON THE TRANSMISSION DYNAMICS OF CHOLERA(2024-10) Alemayehu Animaw NigussieThis research focuses on the development and analysis of a mathematical model to un derstand the transmission dynamics of cholera, a waterborne disease caused by Vibrio cholera. The model divides the population into five compartments: Susceptible (S), Symptomatic Infected (Is), Asymptomatic Infected (Ia), Recovered (R), and Contami nated Environment (B), considering both human-to-human and environment-to-human transmission routes. The threshold parameter R0 = kδβ1λψ+ϵ1λeλψ µkδ(µ+τ1) + kδβ2λϕ+ϵ2λeλϕ µkδ(µ+τ2) is cal culated to assess whether cholera will spread in the population. It is found that if R0 is less than 1, the disease-free equilibrium point is stable, suggesting that cholera can be eradicated under these conditions. Stability analysis of both disease-free and endemic equilibrium points shows that cholera can be controlled when certain conditions, such as reduced infection rates and environmental contamination, are met. Simulations using MATLAB’s ODE45 solver confirm the theoretical results, demonstrating that controlling R0 can effectively manage the disease dynamics. The study identifies key parameters in f luencing R0, including the transmission rates and the impact of therapeutic treatments, providing valuable insights for intervention strategies. The model is based on a system of nonlinear ordinary differential equations that describe the dynamics of the disease in the population. It incorporates therapeutic treatment rates, environmental bacte rial concentration, and different infection categories to represent a more realistic cholera transmission scenario. The research concludes that cholera transmission can be reduced by controlling the following conditions: Lowering the contact rates between susceptible individuals and infected individuals (both symptomatic and asymptomatic) significantly impacts R0. Controlling environmental contamination from infected individuals is cru cial in minimizing disease spread. Effective therapeutic treatments for symptomatic cases can reduce the spread and severity of the disease. This study provides a comprehensive framework for understanding the dynamics of cholera and offers actionable insights for public health strategies aimed at controlling and preventing outbreaks.Item MATHEMATICAL MODELING AND ANALYSIS OF CRIME WITH MEDIA IMPACT(HAWASSA UNIVERSITY, 2024-10) ABDURO MAMU DEKEMAIn this thesis, we proposed and analyzed a nonlinear mathematical model that explains the dynamics of crime that includes media coverage. Some fundamental properties of the model including existence and positivity as well as boundedness of the solutions are investigated. Algebraic expression for the basic reproduction number is computed using the next generation matrix method. The model exhibits two equilibria: the crime-free equilibrium and the persistent equilibrium. The analysis shows that the crime-free equilibrium point is locally asymptotically stable if the basic reproduction number is less than unity (R0 < 1) and the persistent equilibrium point is locally asymptotically stable when the basic reproduction number is greater than one (R0 > 1). It is pointed out that the crime dies out if there is effective media coverage and awareness about crime, otherwise, the crime spreads rapidly in the society and it becomes an epidemic. The Numerical simulation is carried out using Ode45 of Matlab, sensitivity analysis of the basic reproduction number is also constructed. Analytical and numerical result shows that effective use of media coverage is the strategy to reduce the dynamics of crime transmission.