Abstract
Corona virus disease is the most dreaded infectious disease all over the whole world. The outburst of the disease made many researchers to step up with research so as to find solution of eradication of the disease. Jummy et al (2021) developed a compartmental differential equation models which they used in studying direct and indirect transmission of COVID-19.We discovered that their model did not consider quarantine, vaccination and partial immunity. We then incorporated quarantine, vaccination and partial immunity into their models to come up with a modified version of Jummy et al model equations. In this research work, we investigated the positivity of the solution of the modified model, the existence and the uniqueness of the solution. The essence of doing these is to be sure that our models can conform to reality in solving the problem of eradication of COVID-19. We discovered that the solution exist, bounded, unique and positive.