Preventing Smallpox Epidemics Using a Computational Model

By Chintan HossainBy Chintan Hossain and Hiren Patel and Hiren Patel

Facts About Smallpox

Symptoms occur in Symptoms occur in stagesstages

Highly contagious Highly contagious (causes epidemics)(causes epidemics)

Fatal in Fatal in 30% cases30% cases There is a vaccineThere is a vaccine

- Death may occur- Death may occur

GOAL (Objective)

Prevent smallpox epidemics via. Prevent smallpox epidemics via. vaccination.vaccination.

Vaccinate as few as possible because:Vaccinate as few as possible because:

1. Minimize reactions1. Minimize reactions

2. Reduce cost2. Reduce cost

HYPOTHESISHYPOTHESIS: Vaccinating certain percentage : Vaccinating certain percentage of the population may be sufficient to of the population may be sufficient to prevent a smallpox epidemic.prevent a smallpox epidemic.

Stages of Smallpox

Normal (Susceptible)Normal (Susceptible) Immune (or vaccinated)Immune (or vaccinated) IncubationIncubation First StageFirst Stage Early SymptomsEarly Symptoms Late SymptomsLate Symptoms DeathDeath

Vaccination

Contraction

14 days3 days

9 daysR

ecovery

9 days

0.1% chance / day

0.5% chance / day

3.0% chance / day

Normal (Susceptible)

Incubation

Death

First Stage

Late Symptoms

Early Symptoms

ImmuneVaccinated

\

Our Model: Social Networks

Cliques Represent:Cliques Represent:

FamiliesFamilies

WorkplacesWorkplaces

SchoolSchool

Our Society Generator Algorithm

1.1. Use random numbers to pick a family size.Use random numbers to pick a family size.

2.2. Generate a clique of that size.Generate a clique of that size.

3.3. Repeat to create more families.Repeat to create more families.

4.4. Use a similar technique to generate schools Use a similar technique to generate schools and workplaces.and workplaces.

Schools and workplaces connect existing Schools and workplaces connect existing vertices, not new vertices.vertices, not new vertices.

Our Model Comes Alive!

MARKOV GRAPH MARKOV GRAPH + SOCIETY NETWORK+ SOCIETY NETWORK

SIMULATION SIMULATION Advance time 1 dayAdvance time 1 day

Spread DiseaseSpread Disease Advance StagesAdvance Stages DeathDeath

Normal (Susceptible)

Infected Stage

Vaccinated / Immune

Death

FIRST

Spread

EARLY LATE

Incubation

DEAD

Procedure

Run the society generatorRun the society generator Vaccinate Vaccinate kk% of people with most friends % of people with most friends

((vertices with the greatest degree)vertices with the greatest degree) Control: Control: kk = 0% = 0% Variable: Vary percent, Variable: Vary percent, kk, vaccinated , vaccinated

Randomly, infect one person.Randomly, infect one person. Run simulation, and observe results Run simulation, and observe results

(percent infect and length of epidemic)(percent infect and length of epidemic)

OUR PROGRAM

Results

0

0.05

0.1

0.15

0.2

0.25

0 100 200 300 400 500 600 700 800

Time (days)

Fra

ctio

n o

f P

op

ula

tio

n I

nfe

cted

0% Vaccinated

10% Vaccinated

20% Vaccinated

30% Vaccinated

Percent Vaccinated

Length of Epidemic (Days)

0 38210 46920 56630 633

Epidemics Epidemics intensify, intensify, reach a reach a peak, and peak, and then vanishthen vanish

Vaccination Vaccination reduces reduces intensity intensity and speed.and speed.

Results (cont…)

Vaccinating Vaccinating more people more people decreases the % decreases the % infectedinfected

The % infected The % infected becomes small becomes small if over 50% are if over 50% are vaccinated.vaccinated.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Percent Vaccinated

Per

cen

t o

f P

eo

ple

In

fect

ed

Conclusion

Vaccinating 50% of the population Vaccinating 50% of the population effectively effectively prevents epidemicsprevents epidemics..

Vaccinating less than 50% may not prevent Vaccinating less than 50% may not prevent an epidemic, but it an epidemic, but it reducesreduces the the severityseverity and and speedspeed of the epidemic. of the epidemic.

This model can be used for other diseases This model can be used for other diseases by changing the Markov Graph.by changing the Markov Graph.