Teshale Deboch2026-01-292024-11https://etd.hu.edu.et/handle/123456789/369Mathematical modelling is important for better understanding of disease dynamics and developing strategies to manage rapidly spreading infectious diseases. In this thesis, we propose a mathematical model to investigate coronavirus diseases (COVID-19) transmission in the presence of protected and hospitalized classes. Analytical and numerical approach is employed to investigate the results. In the analytical study of the model, we have shown the local and global stability of disease-free equilibrium, existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution and sensitivity analysis of the model is conducted. From these analyses, we found that the disease-free equilibrium is globally asymptotically stable for 𝑅0 < 1 and is unstable for 𝑅0 > 1. A locally stable endemic equilibrium exists for 𝑅0 > 1, which shows the persistence of the disease if the reproduction number is greater than unity. Using sensitivity analysis we establish that 𝑅𝑜 is most sensitive to the rate of Protection of Susceptible individuals 𝜃 and that a high level of protection needs to be maintained as well as hospitalization to control the disease. Finally, we performed numerical simulations using MATLAB software Ode 45 codes to supplement the effectiveness of the analytical findings.en-USCOVID-19ProtectedHospitalizedStability analysis and Sensitivity analysis.Thesis