In this talk, we investigate the global dynamics of a periodic disease transmission model
with two delays in incubation and asymptomatic carriage periods. We first derive the
model system with a general nonlinear incidence rate function by stage-structure. Then,
we identify the basic reproduction ratio $R_0$ for the model and present numerical algorithm
to calculate it. We obtain the global attractivity of the disease-free state when $R_0<1$ and
discuss the disease persistence when $R_0>1$. 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 $R_0$.