The impact of time delay and angiogenesis in a tumor model

We consider a free boundary tumor model under the presence of angiogenesis and time delays in process proliferation, which cell location is incorporated. It assumed that attracts blood vessels at rate proportional to $\alpha$, parameter $\mu$ `aggressiveness' tumor. In this paper, we first prove there exists unique radially symmetric stationary solution $\left(\sigma_{*}, p_{*}, R_{*}\right)$ for all positive $\mu$. Then threshold value $\mu_\ast$ found such linearly stable if $\mu<\mu_\ast$ unstable $\mu>\mu_\ast$. Our results indicate increase $\alpha$ would result reduction $\mu_\ast$; adding delay not alter $\mu_\ast$, but larger tumor, aggressiveness is, greater impact have on size