[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Yixiang Wu (Vanderbilt University)
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Speaker: Yixiang Wu (Vanderbilt University)
Title: On spatial epidemic models and their applications
Abstract: Reaction-diffusion epidemic models are proposed in order to understand how spatial heterogeneity influences the transmission dynamics of infectious diseases. In this talk, I will first present our recent numerical studies of the seasonal influenza epidemics in Puerto Rico based on a diffusive susceptible-infected-recovered model. Our simulations demonstrate that even simple diffusive epidemic models have potential applications in real-world situations. Then I will present our theoretical investigations of a reaction-diffusion vector-host epidemic model. We define a basic reproduction number R0 and show that its magnitude determines the global behavior of the solution of the model: if R0 < 1 the disease free steady state is globally stable; if R0 > 1 the model has a unique globally stable positive steady state. This is joint work with Pierre Magal and Glenn Webb.