SARS-CoV-2(COVID-19) is a very infectious symptomatic and asymptomatic infection caused by Severe Acute Respiratory Syndrome Corona virus 2 (SAR-COV-2). COVID-19 is caused by the SARS-CoV-2 virus, which spreads between people, mainly when an infected person is in close contact with another uninfected person. In this research work, a mathematical model for the novel COVID 19 viral infectious disease which is ravaging the world today including Nigeria was considered.. The mathematical model consists of four different compartments namely, susceptible, infected, vaccine and recovered under convex incident rate. The formulation of the mathematical model and some qualitative aspects for the model including the basic reproductive number of the model, existence of equilibria and its stability results by using various tools of nonlinear analysis were done. On the basis of simulations using Matlab Software package. Dynamical behaviour were observed in the mathematical model due to the vaccine of susceptible and infected individuals or one of those two classes of individuals. The x – rays features of this paper is to formulate and analyse a mathematical model that extends and complements the ones in the literature by incorporating the vaccination class denoted by V(t). Mathematical models are widely used to examine, explain, and state the relevance of the use of vaccines to prevent the spread of the dynamics of infectious diseases (COVID 19) transmission among the Nigerian populace.