Abstract
Oncolytic virotherapy is a promising cancer treatment that uses replication-competent viruses to target and kill tumor cells. Oncolytic alphavirus M1 is a naturally occurring virus which showed high selectivity and potent efficacy in human cancers. Our purpose in this paper is to propose and analyze a model of oncolytic M1 virotherapy with spatial effects and anti-tumor immune response. We investigate the non-negativity and boundedness of solutions for the modified model. We calculate all possible equilibrium points and determine the threshold conditions needed for their existence. One of the equilibria represents the success of the treatment, while the others represent a partial success or a complete fail. We study the global stability of the corresponding equilibrium points by constructing suitable Lyapunov functionals. We also provide the instability conditions of the equilibrium points. We perform some numerical simulations in order to verify the effect of the immune response on oncolytic virotherapy. Our results indicate that the immune response may weaken the effectiveness of oncolytic virotherapy and control the tumor. (C) 2019 Elsevier Inc. All rights reserved.