Persistence of an SEIR Model with Immigration Dependent on the Prevalence of Infection

We incorporate the immigration of susceptible individuals into an SEIR epidemic model, assuming that the immigration rate decreases as the spread of infection increases. For this model, the basic reproduction number, R0, is found, which determines that the disease is either extinct or persistent ultimately. The obtained results show that the disease becomes extinct as R0 < 1 and persists in the population as R0 > 1.