HIV and the Immune System

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# HIV and the Immune System - PowerPoint PPT Presentation

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

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Presentation Transcript

### HIV and the Immune System

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
• 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
Model I- no immune response

dV/dT=aY-bV

dX/dT=c-dX-βXV

dY/dT= βXV-fY

Basic reproductive ratio: R0= βca/dbf

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

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

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

Model II-with immune system

dV/dT=aY-bV

dX/dT=c-dX-βXV

dY/dT= βXV-fY-γYZ

dZ/dT=g-hZ

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

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

AIDS
• HIV-human immunodeficiency virus

▪ attacks CD4+ cells

• AIDS-acquired immunodeficiency syndrome