【摘 要】
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The spatial Susceptible-Infected-Susceptible (SIS) epidemic and Susceptible-InfectedRecovered (SIR) epidemic can be viewed as a critical branching random wa
【机 构】
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University of Chicago
【出 处】
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IMS-China International Conference on Statistics and Probabi
论文部分内容阅读
The spatial Susceptible-Infected-Susceptible (SIS) epidemic and Susceptible-InfectedRecovered (SIR) epidemic can be viewed as a critical branching random walk (BRW) with killing.In this talk, we show how one can use knowledge about BRW to study SIS/SIR epidemic, and discuss the relevant asymptotic properties of BRW.In par ticular, I will talk about the asymptotic behavior of: (1) the number of particles on a "typical" occupied site, (2) the number of occupied si(n)es and (3) the maximal number of particles on a single site.I will also talk about (4) the limiting behav ior of the distribution of all particles ever born during the whole process when the dimension is 2 or 3, which has to do with the local time density of super-Brownian motion.Based on joint work with Steven Lalley.
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