In reaction to the severe socio-economic effects and upheavals that the Covid-19 sickness had on the world within the first few weeks of its introduction, everyone involved had to act quickly to look for possible solutions for preventing the ensuing epidemics. A prompt response is more critical given Nigeria's subpar social, economic, and healthcare infrastructure. Investigated was the efficacy of various pharmacological, non-pharmaceutical, or a combination of both therapies in flattening the Covid-19 incidence curve. In order to investigate the impact of these interventions, a deterministic SVEIHR model was created and applied. The Nigerian Center for Disease Control (NCDC) portal's Covid-19 data were used to parametrize the model. For simulations using a system dynamic simulation, estimated parameters were employed. The fundamental reproduction number, R0, was used to evaluate the success of our suggested intervention in effectively managing COVID-19 transmission. The simulation results demonstrated that the use of only non-pharmaceutical interventions, such as the use of face masks, a light lockdown, and hand washing at baseline or high levels, is insufficient, with the R0 varying from vaccination at the vaccination rate of 0.5% with non-pharmaceutical interventions at any level of compliance, and a combination of vaccination at 0.05% and high hygiene level were effective in flattening the Covid-19 disease incidence curve in Nigeria, returning a R0 less than 1. Furthermore, maintaining a high level of cleanliness, which includes hand washing and the use of a face mask, would be sufficient to stop the spread of Covid-19 disease and eventually flatten Covid-19 disease incidence curve in Nigeria, given a low turnout of 0.05% for vaccination and the easing of lockdown.