Preventing Smallpox Epidemics
Using a Computational Model
By Chintan Hossain
and Hiren Patel
Facts About Smallpox




Symptoms occur in
stages
Highly contagious
(causes epidemics)
Fatal in 30% cases
There is a vaccine
- Death may occur
GOAL (Objective)
Prevent smallpox epidemics via.
vaccination.
 Vaccinate as few as possible because:
1. Minimize reactions
2. Reduce cost

HYPOTHESIS:
Vaccinating certain percentage
of the population may be sufficient to
prevent a smallpox epidemic.
Stages of Smallpox


Late Symptoms
Recovery
9 days

Early Symptoms
9 days

First Stage
3 days

Incubation
14 days

Normal (Susceptible)
Immune (or vaccinated)
Incubation
First Stage
Death
Early Symptoms
Late Symptoms
Death
Contraction

Normal
(Susceptible)
Immune \
Vaccinated
Our Model: Social Networks

Cliques Represent:
Families
Workplaces
School
Our Society Generator Algorithm
1.
2.
3.
4.
Use random numbers to pick a family size.
Generate a clique of that size.
Repeat to create more families.
Use a similar technique to generate
schools and workplaces.

Schools and workplaces connect
existing vertices, not new vertices.
Our Model Comes Alive!
Normal (Susceptible)


MARKOV GRAPH
+ SOCIETY NETWORK
SIMULATION
Advance time 1 day
 Spread Disease
 Advance Stages
 Death
Infected Stage
 Vaccinated / Immune
 Death
Incubation

Spread
EARLY
FIRST

DEAD
LATE
Procedure
Run the society generator
 Vaccinate k% of people with most friends
(vertices with the greatest degree)
 Control: k = 0%
 Variable: Vary percent, k, vaccinated
 Randomly, infect one person.
 Run simulation, and observe results
(percent infect and length of epidemic)

OUR PROGRAM
0.25
Results
Percent
Vaccinated
0
10
20
30


Epidemics
intensify,
reach a
peak, and
then vanish
Vaccination
reduces
intensity
and speed.
Fraction of Population Infected
0% Vaccinated
0.2
Length of
Epidemic (Days)
382
469
566
633
0.15
0.1
10% Vaccinated
0.05
20% Vaccinated
30% Vaccinated
0
0
100
200
300
400
500
Time (days)
600
700
800
Results (cont…)
100

Percent of People Infected
90
80
70
60
50

40
30
20
10
0
0
10
20
30
40
50
60
Percent Vaccinated
70
80
90
100
Vaccinating
more people
decreases the %
infected
The % infected
becomes small
if over 50% are
vaccinated.
Conclusion
Vaccinating 50% of the population
effectively prevents epidemics.
 Vaccinating less than 50% may not prevent
an epidemic, but it reduces the severity and
speed of the epidemic.


This model can be used for other diseases
by changing the Markov Graph.