STOCHASTIC DYNAMICS BETWEEN THE IMMUNE SYSTEM AND CANCER CELLS WITH ALLEE EFFECT AND IMMUNOTHERAPY

Abstract

In this work, we use continuous-time Markov jump processes and the corresponding zero fluctuation ordinary differential equations to analyze the relation between immune response and cancerous cells. We incorporate the Allee effect into our model to show that intrinsic stochasticity and nonlinearity may interact in elimination, equilibrium, and escape mechanisms in the low-count regime. Later, we consider the effect of immunotherapy through a pulse injection term and the Tau-Leaping algorithm. We show using the model state variables and parameters that the cancer cell population at its threshold level gets into the elimination phase for high antigenicity values.