Mathematical Analysis of Models for Tumour Angiogenesis

We deal with well known two mathematical models of tumour angiogenesis. We first review the solvability and the asymptotic profile of the solution to a parabolic ODE system proposed by Othmer and Stevens. Next we consider the model of tumour induced angiogenesis by Anderson and Chaplain in the same line. We modify Anderson and Chaplain model to the same type system of Othmer and Stevens model. This implies a similarity between these models and we can show the existence of global solutions and numerical simulations of Anderson and Chaplain model by using such similarity.