Before revision:  {\it   In the second part, we incorporate in the model, a consideration of artificial herd immunity and show how we can decrease the peak time of infection with a subsequent decrease in the maximum number of infected people . Finally, we estimate a critical value of the rate of vaccination by a statistical method such that we proposed a way of possible eradication of the epidemic in a short time by effectively providing the vaccine to a population .
After revision:  {\it In the second part, we incorporate in the model, a consideration of artificial herd immunity and show how we can decrease the peak time of infection with a subsequent decrease in the maximum number of infected people .