報告題目：Diffusion limit for the partner model at the critical value
報告人：Dr Eric Foxall （University of Alberta）
報告時間：2019年6月12日（星期三）上午9:00-11:00
報告地點：上海理工大學南校區四教414教室
報告摘要：The partner model is an 
epidemic in a population with random formation and dissolution of partnerships, and with disease transmission only occuring within partnerships. Foxall, Edwards, and van den Driessche [7] found the critical value and studied the subcritical and supercritical regimes. Recently Foxall [4] has shown that (if there are enough initial infecteds 
) the extinction time in the critical model is of order 
. Here we improve that result by proving the convergence of 
to a limiting diffusion. We do this by showing that within a short time, this four dimensional process collapses to two dimensions: the number of 
and 
partnerships are constant multiples of the number of infected singles. The other variable, the total number of singles, fluctuates around its equilibrium like an Ornstein-Uhlenbeck process of magnitude 
on the original time scale and averages out of the limit theorem for 
. As a by-product of our proof we show that if 
is the extinction time of 
(on the 
time scale) then 
has a limit.