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The aim of this paper is to develop two delayed SEIR epidemic models with nonlinear incidence rate, continuous treatment, and impulsive vaccination for a class of epidemic with latent period and vertical transition. For continuous treatment, we obtain a basic reproductive number  ℜ   0  and prove the global stability by using the Lyapunov functional method. We obtain two thresholds  ℜ * and  ℜ   ∗  for impulsive vaccination and prove that if  ℜ * < 1, then the disease-free periodic solution is globally attractive and if  ℜ   ∗  > 1, then the disease is permanent by using the comparison theorem of impulsive differential equation. Numerical simulations indicate that pulse vaccination strategy or a longer latent period will make the population size infected by a disease decrease.

Disease Control of Delay SEIR Model with Nonlinear Incidence Rate and Vertical Transmission