Manalebish DebalikeAbebe Monen2025-08-312025-08-312024-09https://etd.aau.edu.et/handle/123456789/7200I develop the SIR models and investigate the stability of their equilibrium points in this paper. Through vaccination strategies and the use of thesis Pontragin Maximum Principle, we are able to control the spread of disease through numerical research and the theory of optimal control. It is discovered that the models' disease-free equilibrium is asymptotically unstable otherwise and asymptotically stable when the fundamental reproduction number is less than one. Additionally, it was discovered that in cases when the fundamental reproduction number is greater than one, the endemic equilibrium is asymptotically stable; in other cases, it is asymptotically unstable. In order to predict and prevent epidemics, this work establishes the susceptible-infectious-recovered (SIR) compartment model for diseaseen-USMathematical ModellingUsing Improved Sir ModelsEnvironmental NoiseThesis