Download Worm modeling — simple epidemic model

Worm modeling —
simple epidemic model
susceptible
# of contacts
infectious
 IS
5
x 10
Simple epidemic model for fixed
population system:
3.5
3
2.5
I(t)
2
1.5
1
0.5
: # of susceptible
: # of hosts
: # of infectious
: infection ability
0
0
100
200
300
t
400
500
600
Analysis of Dynamic Quarantine
I(t): # of infectious
S(t): # of susceptible
T: Quarantine time
R(t): # of quarantined infectious
Q(t): # of quarantined susceptible
1: quarantine rate of infectious
2: quarantine rate of susceptible
Without “removal”:
Assumptions:
Extended
Simple Epidemic Model
Susceptible
S(t)
I(t)
Q(t)=p’2S(t)
# of contacts
Before quarantine:
After quarantine:

R(t)=p’1I(t)
Infectious
Extended
Simple Epidemic Model
x 10
4
x 10
7
7
Original system
Quarantined system
6
6
5
5
4
4
3
3
2
2
1
1
0
0
200
400
600
Time t (second)
800
1000
0
0
4
1
I(t)
R(t)
500 Q(t)
0.8
p'1
500 p'2
0.6
0.4
0.2
200
400
600
Time t (second)
800
1000
0
0
200
400
600
Time t (second)
800
Vulnerable population N=75,000, worm scan rate 4000/sec
T=4 seconds, 1 = 1, 2=0.000023 (twice false alarms per day per node)
R(t): # of quarantined infectious
Q(t): # of quarantined susceptible
Law of large number
1000