2017
DOI: 10.1016/j.heliyon.2017.e00247
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Global dynamics of a colorectal cancer treatment model with cancer stem cells

Abstract: We present and analyze a mathematical model of the treatment of colorectal cancer using a system of nonlinear ordinary differential equations. The model describes the effectiveness of immunotherapy and chemotherapy for treatment of tumor cells and cancer stem cells (CSCs). The effects of CD8+T cells, natural killer cells, and interleukin proteins on tumor cells and CSCs under the influence of treatment are also illustrated. Using the method of localization of compact invariant sets, we present conditions on tr… Show more

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Cited by 7 publications
(4 citation statements)
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“…It has been estimated that 134,490 people in 2016 would be newly diagnosed with CRC in the United States which eventually would claim 49,190 lives [Jansson‐Knodell et al, ]. Though CRC could occur at any age, the the greatest risk for CRC correlates with individuals who are over 50 years old [Abernathy et al, ]. Current treatments for CRC mainly relies on traditional cytotoxic therapy, as well as more recent therapies, such as, the molecular targeted therapy [Loree et al, ].…”
mentioning
confidence: 99%
“…It has been estimated that 134,490 people in 2016 would be newly diagnosed with CRC in the United States which eventually would claim 49,190 lives [Jansson‐Knodell et al, ]. Though CRC could occur at any age, the the greatest risk for CRC correlates with individuals who are over 50 years old [Abernathy et al, ]. Current treatments for CRC mainly relies on traditional cytotoxic therapy, as well as more recent therapies, such as, the molecular targeted therapy [Loree et al, ].…”
mentioning
confidence: 99%
“…Statistics have highlighted that males are more susceptible to CRC than females [ 2 ]. Although CRC can occur at any age, the occurrence of the disease rises greatly with increasing age, and most commonly occurs in individuals over the age of 50 years [ 3 ]. Other risk factors related to lifestyle and dietary factors include high consumption of red or processed meat, obesity, low levels of physical activity, and smoking, all of which are significant risk factors for the occurrence and development of CRC [ 4 ].…”
Section: Introductionmentioning
confidence: 99%
“…Since, in vitro results show that in the early stages the solid tumors grow approximately spherically symmetric [7], in most of the models it is assumed that the tumor grows radially-symmetric. As we mentioned above, treatment of tumors and destroying them is very important, therefore many researchers have investigated the models of tumor growth in which the treatment of tumor is taken into account [10,11,12]. In [10], a mathematical model for the combined treatment of chemotherapy and radiation in Non-Small Cell Lung Cancer patients is developed to improve the treatment strategies for future clinical trials.…”
Section: Introductionmentioning
confidence: 99%
“…In [10], a mathematical model for the combined treatment of chemotherapy and radiation in Non-Small Cell Lung Cancer patients is developed to improve the treatment strategies for future clinical trials. The authors of [11] applied a system of nonlinear ordinary differential equations to analyse a mathematical model of the treatment of colorectal cancer. In the model the effects of immunotherapy and chemotherapy on the tumor cells and cancer stem cells is described.…”
Section: Introductionmentioning
confidence: 99%