Spatiotemporal dynamics of immunogenic tumors

A mathematical model, consisting of a system of two coupled reaction-diffusion partial differential equations describing the interaction between solid tumor and immune system (termed as effector cells), is proposed here. The main focus is on the analysis of the spatiotemporal dynamics of tumor cells and immune cells. The resulting system is analyzed and numerical simulations are presented. Different types of spatial patterns with respect to different initial conditions, and time are observed. Their analysis and mechanism of spatiotemporal pattern formation in immunogenic tumor are studied. Spatiotemporal perturbation around non-spatial steady state beyond the linear regime is obtained based on the analysis of higher-order perturbation terms.