时间：2023年8月17日，21:30-23:00
地点：线上腾讯#144-356-043、密码893347；线下1C207
主讲人: 舒洪英，教授，陕西师范大学
题目：Viral infection dynamics：a global analysis
摘要：First, we consider an in-host model with distributed delay to describe the in vivo infection dynamics of many viruses such as HIV-I, HCV, and HBV. We prove that the viral dynamics are determined by the basic reproduction number for infection. We also demonstrate that intracellular delays will lead to periodic oscillations in in-host models only with the right kind of target-cell dynamics. Next, we consider a viral model with the cytotoxic T lymphocyte (CTL) response. This general model admits three types of equilibria: infection-free equilibria, CTL-inactivated infection equilibria, and CTL-activated infection equilibria. We prove that the viral dynamics are determined by two threshold parameters: the basic reproduction number for infection and the basic reproduction number for immune response. We further incorporate two infection modes (virus-to-cell mode and cell-to-cell mode) into the viral infection model. Finally, we propose a general model to investigate the joint impact of viral diffusion and cell-to-cell transmission on viral infection dynamics. The mathematical challenge lies in the fact that the model system is partially degenerate and the solution map is not compact. By an innovative construction of Lyapunov functionals, we demonstrate that the basic reproduction number is the threshold parameter which determines global picture of viral dynamics.
主讲人简介：舒洪英，陕西师范大学数学与统计学院教授，博士生导师。2016年获上海市浦江人才计划，2017年获陕西省百人计划。主持2项国家自然科学基金项目，1项上海市自然科学基金项目和1项加拿大科研基金项目。主要研究微分动力系统及生物数学方面的应用。已在J. Math. Pures Appl., Journal of Differential Equations, SIAM Journal of Applied Mathematics, JDE, JDDE, JMB,BMB等国际专业领域发表SCI论文四十余篇。
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