报告题目：Diffusion limit for the partner model at the critical value
报告人：Dr Eric Foxall （University of Alberta）
报告摘要：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  found the critical value and studied the subcritical and supercritical regimes. Recently Foxall  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.