Abstract: The author considers a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate insider them, and eventually cause their death. As
infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. This process is modelled as a free boundary problem for a nonlinear system of hyperbolic differential equations, where the free boundary is the surface of the tumor. The unknowns are the densities of uninfected cells, infected cells, necrotic cells and the free virus particles, and the velocity of cells within the tumor as well as the free boundary r=R(t). The aim of this paper is to explore the conditions under which the tumor can be made to shrink to zero.

Key words: Tumor, Replication-competent virus, Hyperbolic system, Free boundary problem.