Effect of vaccination on mathematical modeling of covid-19

Corona virus 2019 (Covid-19) have been endemic both in Africa and the whole world. In this paper we have formulated and analyze mathematical model of covid-19 that monitors the temporal dynamics of the disease in the presence of preventive vaccine since the most effective ways of controlling the transmission of infection disease is through vaccination and treatment. Due to transmission characteristics of covid-19, we have divided the population into six classes. That is; susceptible(S), vaccinated (V), infective (I), hospitalized (H), home based care (HB ) and recovery(R). We have formulated non-linear system of differentials equation governing the model to compute and solve using quantitative analysis. Feasibility region, positivity of model variable, disease free equilibrium and local stability of the model are discussed. The solution has been computed using numerical classical fourth order Runge Kutta integration method to gauge its effectiveness. The model monitor reproduction number ROwhich describe the dynamics of the Covid-19.The disease fee equilibrium is local asymptotically stable when Ro<1 and unstable when   Ro>1. MAPLE will be used to carry out the simulation and graphical results, then presented and discussed to explain the solution of the problem.