Mathematical modelling of Covid-19 with the effect of vaccine

Covid-19 is the most recently discovered infectious disease affecting the countries all around the world. SARS-CoV-2, which is a member of coronavirus family, is the virus that makes the infection. Until the 28th of September 2020, almost 34 million people infected by the virus and more than 1 million people died all around the world. One of the most discussed ideas about the disease to die out is vaccination. In our study, we tried to analyze this idea and show the effect of vaccine for Covid-19. Our work starts with constructing an SVI mathematical model. Afterwards, we made the analyze of our model. Then, by taking into consideration of incoming passengers and precautions that should be taken, we used the vaccination idea with changing the percentage of vaccinated people in a population. In last section, we used numerical simulations to support our idea. In our work, we conclude that vaccination is substantially effective if we consider the other things that affect the disease which is incoming passengers and precautions like wearing mask, maintaining social distance, etc.