Dynamic analysis of cancer-immune system with Allee effect

Wang, Cuiping (2021) Dynamic analysis of cancer-immune system with Allee effect. Masters thesis, Memorial University of Newfoundland.

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Abstract

There are numbers of mathematical models to describe the relation between immune effector cells and cancer cells. The purpose of this thesis is to explore the influence of Allee effect on immune effector cells and cancer cells. First, we introduce some background information of how the immune system inhibit and suppress cancer growth and Allee effect. In Chapter 2, we propose a general model to describe the interaction between immune effector cells and cancers. We discuss some basic dynamical properties of the system under strong Allee effect and weak Allee effect with linear functional responses. For instance, the existence of equilibrium points and their local stabilities. In Chapter 3, using Matlab code, we do sampling-based sensitive analysis on the density of cancer cells. Sensitive analysis can narrow down the parameter of interest and suggest the most significant parameter that affect the density of cancer cells. In Chapter 4, due to the difficulty of solving the explicit form of positive equilibrium point. We give numerical simulation to explore the existence of positive equilibrium points and their stabilities. At last, in Chapter 5, we summarize the results in this thesis, and indicate some problems for future work.

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