题目：Qualitative Analysis of Switched Epidemic Models

报告人：Prof. Xinzhi Liu (University of Waterloo Canada)

地点：致远楼103室

时间：2024年5月20日 星期一 10：00-11：00

摘要：Mathematical models are vital for implementing, evaluating, and optimizing control schemes in order to eradicate a infectious disease. These mathematical models may be oversimplified, but they are useful for gaining knowledge of the underlying mechanics driving the spread of a disease, and for estimating the number of vaccinations required to eradicate a disease. This talk introduces a switched epidemic model considering changing contact rates in an infected society. It also takes into account the presence of vulnerable individuals as frontiers in vaccination, recognizing their societal importance. The qualitative analysis of the model involves results on the positive invariance set and the positivity of the solutions. Additionally, stability criteria are established, where the basic reproduction number is considered as a bifurcation value. Numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

刘新芝教授现任加拿大滑铁卢大学应用数学系教授。1988年在美国德克萨斯大学阿灵顿分校获博士学位。于1990年受聘滑铁卢大学并于1994年被聘为该校终身教授。

刘新芝教授是国家教育部"长江学者奖励计划"（第三批）特聘教授，于2001年元月受聘于华中科技大学.

刘教授的研究方向包括:混合动力系统,非线性系统控制及稳定性,复杂网络的同步,保密通讯,传染病模型等。已发表学术论文400余篇，学术专著6部, 学术编著20余部。

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