Abstract—This paper investigates a simple SIVS (susceptible–infected–vaccinated–susceptible) disease transmission model with immigration of susceptible and vaccinated individuals. We show global stability results for the model, and give an explicit condition for the existence of backward bifurcation and multiple endemic equilibria. We examine in detail how the structure of the bifurcation diagram depends on the immigration. Keywords-vaccination model with immigration; backward bifurcation; stability analysis I