Bifurcation and Stability of a Mathematical Model for Tumor Growth with Oncolytic Virotherapy

Replication-competent viruses have been used as an alternative therapeutic approach for cancer treatment. In this paper, a T-OV-taxis mathematical model for tumor growth with oncolytic virotherapy is established. First, the stability of u* is studied in the ODE system and in the reaction-diffusion system of the model. It is found that the stability of u* will not be changed by diffusion alone. Next, the T-OV-taxis rate chi is selected as a bifurcation factor, and a threshold value chi(0) (chi(0) < 0) is found, such that positive constant steady-state u* becomes unstable when chi < chi(0). Hence, the taxis-driven Turing instability occurs. Furthermore, the existence, stability, turning direction of steady-state bifurcation are discussed. And, the local steady-state bifurcation is extended to a global one, where the theory used is the Crandall-Rabinowitz bifurcation theorem. Finally, it is concluded that T-OV-taxis rate chi plays an important role in this mathematical model.