1 / 15

HIV and the Immune System

HIV and the Immune System. Janet Cady. Introduction. Modeling the relationship between the immune system and viruses Two models: ▪ without immune system ▪ with immune system Why HIV is good at getting past the immune system. Viruses. Aren’t capable of reproducing on their own

shaun
Download Presentation

HIV and the Immune System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. HIV and the Immune System Janet Cady

  2. Introduction • Modeling the relationship between the immune system and viruses • Two models: ▪ without immune system ▪ with immune system • Why HIV is good at getting past the immune system

  3. Viruses • Aren’t capable of reproducing on their own • Invade host cells and use cellular machinery to replicate their own DNA • When new viruses are mature, burst out of cell, results in death of cell

  4. Model I- no immune response dV/dT=aY-bV dX/dT=c-dX-βXV dY/dT= βXV-fY Basic reproductive ratio: R0= βca/dbf Virus spreads if R0>1

  5. Nondimensionalization x=(d/c)X, y=(d/c)Y, v=(bf/ac)V, t=dT dx/dt=1-x- R0xv dy/dt=R0xv-αy εdv/dt= αy-v ε=d/b α=f/d

  6. Steady States 0=(αy-v)/ ε v*= αy* 0=1-x- R0xv x*=1/(1+ R0v*) 0=R0xv-αy x*=1/R0 x*=1/R0 y*=1/ α(1- 1/R0) v*=1- 1/R0

  7. Immune System • B Cells: made in bone ▪ Produce antibodies ▪ Kill free viruses • T Cells: made in Thymus gland ▪ Helper T cells- alert cytotoxic cells ▪ Cytotoxic killer cells- kill infected cells

  8. Model II-with immune system dV/dT=aY-bV dX/dT=c-dX-βXV dY/dT= βXV-fY-γYZ dZ/dT=g-hZ

  9. Nondimensionalization z=hZ/g dx/dt=1-x- R0xv εdv/dt= αy-v dy/dt=R0xv-αy-kyz dz/dt=λ(1-z) k= γg/dh λ=h/d

  10. Steady States x*=1/R’0 y*=1/(α+k)(1- 1/R’0) v*= α /(α+k)(1- 1/R’0) z*=1 R’0=(α /(α+k)) R0

  11. AIDS • HIV-human immunodeficiency virus ▪ attacks CD4+ cells • AIDS-acquired immunodeficiency syndrome ▪ advanced stage of HIV ▪ fewer than 200 CD4+ cells/mm3 blood • Opportunistic infections

  12. References • Knorr, A.L., Srivastava,R. (2004) Evaluation of HIV-1 kinetic models using quantitative discrimination analysis. Bioinformatics. 21(8) 1668-1677. • Britton, N.F. (2003) Essential Mathematical Biology. Springer-Verlag, London. 197-201.

More Related