加拿大阿尔伯特大学Eric Foxall博士学术报告(三)

发布者:姜珍珍发布时间:2019-06-10浏览次数:57

报告题目:Diffusion limit for the partner model at the critical value

报告人:Dr Eric Foxall University of Alberta

报告时间:2019612日(星期三)上午9:00-11:00

报告地点:上海理工大学南校区四教414教室

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 [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.


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