[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Zhisheng Shuai (University of Central Florida)
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- Open to the public
Speaker: Zhisheng Shuai (University of Central Florida)
Title: Modeling infectious diseases: global dynamics for disease endemicity and elimination
Mathematical models have been used to enhance our understanding in the transmission and spread of infectious diseases. Mathematical investigation of these epidemiological models can assist public health authorities to make better designs and evaluations of disease prevention and control strategies. However, the complexity and heterogeneity in the disease transmission process often pose a serious mathematical challenge for the analysis of disease dynamics. Specifically, could the disease be completely eliminated by certain public health interventions, or still persist at a positive (endemic) level? We will show how a complex disease model can be viewed as a dynamical system defined on a transmission-transfer network (digraph), and how a graph-theoretic approach to Lyapunov functions developed by Guo-Li-Shuai can be applied to establish the global disease dynamics. In particular, when the transmission-transfer network is of hierarchical structure, graph reduction can provide a key to the successful application of the approach.