Transcript AIDS and the S-I

AIDS and the S-I-R Model
A study of three groups of people most
susceptible to the AIDS virus
A Presentation by Tiana Towns and Tanya Milki
Objective
 Create an SIR model that realistically
predicts AIDS movement throughout the
given populations
The key issues and themes
 The main issue in this project was
determining the transmission coefficient
that would give us realistic, feasible
results
 Finding statistical data to help us create
realistic models
The General SIR Model
 S’(t)=-aS(t)I(t)
 I’(t)=aS(t)I(t)-bI
 R’(t)=bI
Our tweaked model…
 S’(t)=-aS(t)I(t)
 I’(t)=aS(t)I(t)-bI
 D’(t)=bI
General assumptions
 Everyone who has the virus eventually
dies
 We are only working with fixed
populations
 No natural disasters will compromise our
model
 No cure will be found
Male-to-male homosexual contact
7000000
6000000
5000000
Series1
4000000
Series2
3000000
Series3
2000000
1000000
0
0
10
20
30
40
50
60
Injected drug users
2000000
1800000
1600000
1400000
1200000
Series1
1000000
Series2
800000
Series3
600000
400000
200000
0
0
10
20
30
40
50
60
Heterosexual contact
140000000
120000000
100000000
Series1
80000000
Series2
60000000
Series3
40000000
20000000
0
0
10
20
30
40
Conclusions
 We are only able to make speculations
as to how the AIDS epidemic will spread
in the coming years because of the
uncertainties in information, such as
population sizes, those not taken into
account for, those belonging to more than
one susceptible population, etc.