In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discre...In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion 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 effec- tiveness 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.展开更多
基金This work is supported by the National Natural Science Foundation of China under Grant 61174039. The authors would like to thank the editor and reviewers for their hard work to the improvement of the quality of this paper.
文摘In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion 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 effec- tiveness 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.
