Simulation of a Model of Tumors with Virus-therapy.

We consider a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate inside them, and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. However, a major factor influencing the efficacy of virus agents is the immune response that may limit the replication and spread of the replication-competent virus. The immune response is cytokine-mediated. The expression of viruses in tumor cells sensitize cells to lysis by the TNF (tumor necrosis factor) cytokine. The competition between tumor cells, a replication-competent virus and an immune response is modelled as a free boundary problem for a nonlinear system of partial differential equations, where the free boundary is the surface of the tumor. In this model, the immune response equation is a non-standard parabolic equation due to the chemotaxis (spatial gradients of diffusible chemicals) of the immune response. The purpose of this paper is to give the numerical methods for solving this kind of free boundary problems. Several simulation results are also given. [ABSTRACT FROM AUTHOR]