Abstract
In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination is investigated. In vaccination strategy, we perform impulsive vaccination of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effectiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput. Simulat.79 (2009) 3038–3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.
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