In this paper, the global dynamics of a periodic disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. We first derive the model system with a general nonlinear incidence rate function by stagestructure. Then, we identify the basic reproduction ratio R0 for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the diseasefree state when R0 < 1 and discuss the disease persistence when R0 > 1. We also explore the coexistence of endemic state in the nonautonomous system and prove the uniqueness with constants coefficients. Numerical simulations are provided to present a case study regarding the meningococcal meningitis disease transmission and discuss the influence of carriers on R0.

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