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APPENDIX B. SUPPLEMENT TO CHAPTER 6 Figure B.2: Stable points for Matrix 5 with α 32 = 2 . 0. Interestingly, for Matrix 6 (Figure B.3), in order to increase the value of α 32 above 1 . 0 while maintaining the inequalities, α 13 (the competition of T − cells on T + cells) also had to be increased. In this way, the value of α 13 is set to 2 . 0 and α 32 is set to 1 . 5. Because the T − cells now have a significant competitive affect on T + cells, the stability points that contain T − cells have quite low to zero densities of T + cells. Figure B.3: Stable points for Matrix 6 with α 13 = 2 . 0 and α 32 = 1 . 5. A stable point from every stable region from each of the updated matrices is displayed in Table B.1. The stable points for Matrix 2 are discussed in detail in Chapter 6, while the remaining stable points are discussed in further supplemental sections. 140

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