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.

[img] [English] PDF - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (1MB)


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.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/15127
Item ID: 15127
Additional Information: Includes bibliographical references (pages 37-40).
Keywords: Allee Effect, Cancer-immune system, Sensitive Analysis, Stability, Dynamic
Department(s): Science, Faculty of > Mathematics and Statistics
Date: October 2021
Date Type: Submission
Digital Object Identifier (DOI): https://doi.org/10.48336/809G-4N18
Library of Congress Subject Heading: Allee effect; Cellular immunity--Mathematical models; Cancer cells--Mathematical models.

Actions (login required)

View Item View Item


Downloads per month over the past year

View more statistics