Invited by Prof. Zhicheng Wang and associate Prof. Jianwen Sun of School of Mathematics and Statistics, Prof. Zejia Wang fromJiangxi Normal Universitywill give a lecture online.

Title：The impact of time delay and angiogenesis in a tumor model

Time：10:00 a.m.,Dec. 9th, 2021

Conference ID：423 657 642( Tencent Conference)

Abstract：

We consider a free boundary tumor model under the presence of angiogenesis and time delays in the process of proliferation, in which the cell location is incorporated. It is assumed that the tumor attracts blood vessels at a rate proportional to \alpha, and a parameter /mu is proportional to the “aggressiveness” of the tumor. We first prove that there exists a unique radially symmetric stationary solution (\delta*, p*, R*)for all positive \alpha,\mu.Then a threshold value \mu*is found such that the radially symmetric stationary solution is linearly stable if

\mu < \mu* and linearly unstable if \mu > \mu* . Our results indicate that the increase of the angiogenesis parameter \alpha would result in the reduction of the threshold value \mu*, adding the time delay would not alter the threshold value \mu* but would result in a larger stationary tumor, and the larger the tumor aggressiveness parameter \mu is, the greater impact of time delay would have on the size of the stationary tumor.