报告摘要: In this presentation, 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 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.

报告时间：2023年9月9日（周六）上午9:30-11:00

报告地点：数学系报告厅主楼203

报告人简介：

袁沅教授, 1984年于武汉大学获得学士学位，1988年于中南大学获得硕士学位，2002年于加拿大西安大略大学获得博士学位。2002年9月起受聘于加拿大纽芬兰纪念大学至今，现为该校数学与统计系终身正教授和博士生导师。袁教授主要研究方向包括非线性动力系统的稳定性及分支分析、时滞微分方程及其在神经网络和生物数学等的应用、微分方程的符号及数值计算方法，研究一直受到加拿大NSERC的资助。现已在SIAM J. Appl. Math., SIAM J. Appl. Dyn. Syst., J. Differential Equations, J. Math. Biol., J. Math. Anal. Appl.等应用数学及生物数学杂志发表论文60余篇。