Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor-immune interactions

In this paper, we introduce a stochastic partial differential equation model for the spatial dynamic of tumor-immune interactions. We perform numerical simulations in order to investigate the propagation of traveling waves in model system under the influence of random space-time fluctuations. One of methods is to solve a stochastic partial differential equation system for tumor-immune cell densities. The second method is to solve a stochastic partial differential algebraic equation system in order to assess the wave behavior of the solution in comparison with the deterministic approach. Finally, we discuss the implications of the model results.