LAUSR

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 stage-structure. Then, we identify the basic reproduction ratio $${\mathcal {R}}_0$$R0 for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when $${\mathcal {R}}_0<1$$R0<1 and discuss the disease persistence when $${\mathcal {R}}_0>1$$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 $${\mathcal {R}}_0$$R0.