In this paper, a deterministic compartmental model is presented to assess the impact of vaccination and non-pharmaceutical interventions (social distance, awareness, face mask, and quarantine) on the transmission dynamics of COVID-19 with co-morbidity and re- infection. An expression for the basic reproduction number is then derived for this model. Theoretical analysis shows that the model exhibits backward bifurcation phe- nomenon when the basic reproduction number is less than unity. But for the case of no re- infection, the model has a globally asymptotically stable disease-free equilibrium (DFE) when the basic reproduction number is less than unity. Furthermore, it is shown that in the case of no re-infection, a unique endemic equilibrium point (EEP) of the model exists which is globally asymptotically stable whenever the reproduction number is greater than unity. From the global sensitivity and uncertainty analysis, we have identified mask coverage, mask efficacy, vaccine coverage, vaccine efficacy, and contact rate as the most influential parameters influencing the spread of COVID-19. Numerical simulation results show that the use of effective vaccines with proper implementation of non-pharmaceutical interventions could lead to the elimination of COVID-19 from the community. Numerical simulations also suggest that the control strategy that ensures a continuous and effective mass vaccination program is the most cost-effective control strategy. The study also shows that in the presence of any co-morbidity and with the occurrence of re-infection, the disease burden may increase