1. The Relationship Between T-Cells and HIV Progression Kiran Dhillon and Kelly Nuibe

2. Courtesy of http://webs.wichita.edu/mschneegurt/biol103/lecture15/hiv_cellbinding.gif HIV: Human Immunodeficiency Virus T Cell

3. Biological Variables and Parameters V = virus particles I = productively infected cells P = rate per cell C = clearance rate

4. Predator-Prey Models  Target T-Cell Limitation: Logistic Model Activated T Cell Model  Immune Control Model Courtesy of http://www.epidemic.org/theFacts/images/deformationOfRC.gif

5. The Logistic Model (as seen in class)

6. Target T Cell Limitation: Logistic Model T = target cells I = productively infected cells V = equation 1 β = true infection rate (cells per particle per day) δ1 = 0.5 day -1, turnover rate of productively infected T cells γ = combines all other virus induced depletion of the CD4 T cells α = 0.1 day -1 rate of increase; the max rate of T cell renewal T max = 1000 cells µ L -1, non-infected steady state CD4 count T tot = T+I

7. Target T Cell Limitation: Activated T Cell Model T = activated CD4 cells α Q = rate at which quiescent T cells are activated δ Q = rate they die at β = rate at which activated CD4 cells are infected by virus r = rate at which activated CD4 cells revert back to the quiescent state 2rT/(1+T tot /T max ) = defines a density dependent regulation of the proliferation rate T tot = Q+T+I

8. Immune Control Model Courtesy of http://www.karencarr.com/Images/Gallery/2004_gallery_steggy_and_allosaur.jpg VIRUS Immune Response (CD8 Cells, aka “Killer Cells”)

9. Immune Control (continued) When V is at an equilibrium state Ē = pβ/cK, E: cytotoxic effector T cells

10. T-Cell Count and HIV Progression