Mathematical analysis on a diffusion model describing the compatibility between two types of tumor cells

Abstract

Cancer caused by malignant tumor is a very common and serious disease which can lead to people towards death. However, sometimes, cancer may be controlled if the cancer cells can be infected and split by particular virus with weak pathogenicity. To give a better understanding on tumor dynamics, in this paper, we deal with a reaction–diffusion tumor model, which comes from the process of tumor therapy with oncolytic virus. Our main objective is to analyze the biological compatibility of uninfected and infected tumor cells. In addition, we are concerned with the long‐time behavior, stability, and a priori estimates for the model. The compatibility conditions show that under certain range of parameters control, the infected tumor cells can coexist with normal tumor cells or be eliminated by oncolytic virus as time goes on; in the elimination case, it implies that the organism's complete recovery is highly possible as a result of the attack of oncolytic virus. An indirect idea in calculating fixed point index is proposed; correspondingly, a new condition on coexistence is presented.