Si Tang : Spatial SIR model and superprocesses

Posted by Shuwen Lou , part of the Statistics and Data Science Seminar.

At

Nov. 16, 2016, 4 p.m.

In

SEO 636

Abstract

The classic Susceptible-Infected-Resistant (SIR) model, due to Kermack & McKendrick (1927), describes the spread of an infectious disease in an infinite, homogeneous population using a system of ordinary differential equations. In this talk, I will focus on stochastic SIR models, where the population is of size $N$ and transmissions only occurs locally. In these models, the sizes of infected clusters are characterized by the excursion lengths of a continuous stochastic process, denoted by $W_t$. In particular, in the mean-field SIR case, $W_t$ is a reflected (at 0) Brownian motion with negative drift; in the spatial case, $W_t$ is a reflected Brownian motion trimmed by a Poisson point process whose intensity is determined by a super Brownian motion with time-and-location dependent killing.

TBA