1. Preventing Smallpox Epidemics Using a Computational Model By Chintan Hossain and Hiren Patel

2. Facts About Smallpox Symptoms occur in stages Symptoms occur in stages Highly contagious (causes epidemics) Highly contagious (causes epidemics) Fatal in  30% cases Fatal in  30% cases There is a vaccine There is a vaccine - Death may occur

3. GOAL (Objective) Prevent smallpox epidemics via. vaccination. Prevent smallpox epidemics via. vaccination. Vaccinate as few as possible because: 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.

4. Stages of Smallpox Normal (Susceptible) Normal (Susceptible) Immune (or vaccinated) Immune (or vaccinated) Incubation Incubation First Stage First Stage Early Symptoms Early Symptoms Late Symptoms Late Symptoms Death Death Vaccination Contraction 14 days 3 days 9 days Recovery 9 days 0.1% chance / day 0.5% chance / day 3.0% chance / day Normal (Susceptible) Incubation Death First Stage Late Symptoms Early Symptoms Immune Vaccinated \

5. Our Model: Social Networks Cliques Represent: Cliques Represent:FamiliesWorkplacesSchool

6. Our Society Generator Algorithm 1. Use random numbers to pick a family size. 2. Generate a clique of that size. 3. Repeat to create more families. 4. Use a similar technique to generate schools and workplaces.  Schools and workplaces connect existing vertices, not new vertices.

7. Our Model Comes Alive! MARKOV GRAPH + SOCIETY NETWORK MARKOV GRAPH + SOCIETY NETWORK SIMULATION SIMULATION Advance time 1 day Advance time 1 day  Spread Disease  Advance Stages  Death Normal (Susceptible) Infected Stage Vaccinated / Immune Death  FIRST Spread EARLY LATE Incubation DEAD 

8. Procedure Run the society generator Run the society generator Vaccinate k% of people with most friends (vertices with the greatest degree) Vaccinate k% of people with most friends (vertices with the greatest degree)  Control: k = 0%  Variable: Vary percent, k, vaccinated Randomly, infect one person. Randomly, infect one person. Run simulation, and observe results (percent infect and length of epidemic) Run simulation, and observe results (percent infect and length of epidemic)

9. OUR PROGRAM

10. Results Epidemics intensify, reach a peak, and then vanish Epidemics intensify, reach a peak, and then vanish Vaccination reduces intensity and speed. Vaccination reduces intensity and speed.

11. Results (cont…) Vaccinating more people decreases the % infected The % infected becomes small if over 50% are vaccinated.

12. Conclusion Vaccinating 50% of the population effectively prevents epidemics. 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. 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. This model can be used for other diseases by changing the Markov Graph.