# 特邀加拿大纽芬兰纪念大学袁沅教授来我校作报告

In this talk, 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 $\mathcal{R}_0$ for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when $\mathcal{R}_0<1$ and discuss the disease persistence when $\mathcal{R}_0>1$. 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 $\mathcal{R}_0$.

数学与统计学院

2019年9月12日