报告题目：Global threshold dynamics and finite-time contraction stability for age-structured HIV models with delay

报告人：张启敏

报告时间：2022年12月12日20：30-22：30

腾讯会议ID：994-465-977

报告摘要：Considering age of infected cells and intracellular delay in both virus-to-cell and cell-to-cell transmissions, we develop an age-structured HIV model with delay to investigate the global threshold dynamics, which show the uninfected and infected steady states of the model. Using the Lyapunov function and LaSalle's invariance principle, we show that the global threshold dynamics of the model can be determined by utilizing basic reproduction number. Moreover, given that sudden environmental changes can lead to uncertainty in parameters of the model, a stochastic age-structured HIV model with Markovian switching is developed to study the finite-time contraction stability, which characterizes transmission properties of virus over a finite time. The sufficient conditions of the finite-time contraction stability are obtained by employing the Lyapunov function and stochastic comparison theorem. Numerical examples are presented to illustrate the theoretical results, and numerical results show that different noise intensity and delay affect stability of the HIV models.

报告人简介：宁夏大学数学统计学院二级教授，博士研究生导师，宁夏自治区313人才。中国生物数学学会常务理事，中国人口学会理事和宁夏统计学会理事。长期以来一直从事随机种群模型、流行病模型及生态模型动力学、最优控制及数值计算理论研究工作。主持国家自然基金4项、国家社科基金1项、宁夏自然基金目4项及宁夏重点研发项目1项。在科学出版社出版学术专著3部，发表论文100余篇。