讲座题目：A periodic disease transmission model with asymptomatic carriage and latency periods 主讲人：袁沅 教授 主持人：何小清 研究员 开始时间：2019-11-15 13:30:00 讲座地址：闵行数学楼102 主办单位：数学科学学院
报告人简介： 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。现已在SIAM Journal of Applied Mathematics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Journal of Differential Equations, Nonlinear Analysis: Real World Applications, SIAM Journal on Applied Dynamical Systems等主要应用数学及生物数学杂志发表论文近六十篇。研究成果深受同行好评及引用，研究一直受到加拿大NSERC的资助。 报告内容： 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 $\mathcal{R}_0$. |
