报告题目：Some results on two types of delayed HIV virus-to-cell models with Beddington-DeAngelis incidence and reactivation of latent infection

报告人：张龙，新疆大学数学与系统科学学院教授

报告时间： 2023年9月5日 上午9：00- 10：00

报告地点： 数学楼2-3

报告摘要: In this talk, two types of HIV virus-to-cell models with delays and Beddington-DeAngelis functional response, latent infection, and logistic growth are proposed respectively. Using the characteristic equations and analytical means, the principle reproduction number R₀ on the local stability of infection-free and chronic infection equilibria of two models are established. Furthermore, by constructing suitable Lyapunov functionals and using LaSalle invariance principle, we show that if R₀ ≤ 1 the infection-free equilibrium is globally asymptotically stable, while if R₀ > 1 the chronic -infection equilibrium is globally asymptotically stable. Comparing the effects between discrete and distributed delays on the stability of HIV virus-to-cell dynamical models, we can see that they could be same and different even opposite. For HIV virus-to-cell model with latent infection and logistic growth, we find the delays have great influence on stability of equilibrium, which could switch the state from stability to un-stability until bifurcation.

张龙教授简介： 新疆大学数学与系统科学学院教授，博士生导师。1997.9-2007.6 于新疆大学数学与系统科学学院完成本科、硕士、博士阶段学习，导师：滕志东教授。2010.9 -2011.9 国家留学基金委公派赴美国迈阿密大学从事博士后研究工作，合作导师：阮士贵教授。主要从事微分方程理论及其应用、生物数学模型研究。主持国家自然科学基金项目 4 项，自治区各类自然科学基金项目 9项。在“Math. Biosci.”“J. Theoret. Biol.”“Stud. Appl.Math.”“Nonl. Anal.:RWA”“Appl. Math. Lett.”“Int. J. Bifur. Chaos.”“J. Math. Anal. Appl.”“Appl. Math. Model.”等 SCI 收录期刊发表 70 余篇。获得自治区自然科学奖一等奖、自治区科技进步奖二等奖各1次；获自治区自然科学优秀论文奖一等奖 1 次，二等奖 2 次。入选自治区“天山英才”第二层次人选、自治区优秀青年科技创新人才称号。