Alemayehu Animaw Nigussie2026-01-292024-10https://etd.hu.edu.et/handle/123456789/355This 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.en-USCholeraBacteria GrowthReproduction NumberStabilityModelingSensitivity AnalysisNumerical SimulationThesis