Effects of the killing rate on global bifurcation in an oncolytic-virus system with tumors

Oncologists and virologist are quite concerned about many kinds of issues related to tumor-virus dynamics in different virus models. Since the virus invasive behavior emerges from combined effects of tumor cell proliferation, migration and cell-microenvironment interactions, it has been recognized as a complex process and usually simulated by nonlinear differential systems. In this paper, a nonlinear differential model for tumor-virus dynamics is investigated mathematically. We first give a priori estimates for positive steady-states and analyze the stability of the positive constant solution. And then, based on these, we mainly discuss effects of the rate of killing infected cells on the bifurcation solution emanating from the positive constant solution by taking the killing rate as the bifurcation parameter.