Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Abstract

Immunotherapy is one of the future treatments applicable in most cases of cancer including malignant cancer. Malignant cancer usually prevents some genes, e.g., p53 and pRb, from controlling the activation of the cell division and the cell apoptosis. In this paper, we consider the interactions among the cancer cell population, the effector cell population that is a part of the immune system, and cytokines that can be used to stimulate the effector cells called the IL-2 compounds. These interactions depend on both time and spatial position of the cells in the tissue. Mathematically, the spatial movement of the cells is represented by the diffusion terms. We provide an analytical study for the constant equilibria of the reaction-diffusion system describing the above interactions, which show the initial behaviour of the tissue, and we conduct numerical simulation that shows the dynamics along the tissue that represent the immunotherapy effects. In this case, we also consider the steady-state conditions of the system that show the long-time behaviour of these interactions.

Theoretical study and numerical simulation for a mathematical model of diffusive cancer with effect of stem cell therapy and chemotherapy

“…For example, references [15,18] introduced a mathematical model to describe the interaction between the tumor and the immune therapy. Suddin et al [22] studied the interactions between the tumor, the immune system, effector cells and the cytokine Interleukine-2 ( IL-2) treatment with spread cells by modeling a three-dimensional system of partial differential equations (PDEs) that subjects to initial and boundary conditions. The reference [26] studied the cancer model with immune therapy that containing interleukine-10 (IL-10) and anti-PD-L1 inhibitor.…”