2013 Pacific Undergraduate Research and Creativity Conference (PURCC)

Title

Pandemic at Pacific

5

Lead Author Major

Applied Math and Physics and Biological Sciences

Format

Poster Presentation

John Mayberry

Mathematics

Abstract/Artist Statement

The classic SIR model for disease spread utilizes a system of ODE'S that assume a population is well mixed and displays some homogenous behavior. In this project we investigate how accurate this assumption is by comparison with a more realistic Network Model for disease spread. For the Network Model we came up with four different possible degree distributions: Uniform, Power Law, Binomial, and Bimodal Binomial. We found that the ODE model severely overestimates both the size of the outbreak and its duration. The difference between the 4 distributions was not as large as the ODE model; the largest difference was a 20% higher number of total infected in the Binomial versus the Power Law distribution. Next, we investigated the effect of a limited amount of vaccinations on different networks (specifically Binomial and Power Law). We proposed 3 possible vaccination strategies: 1. Target vaccinations to those with the highest number of unvaccinated connections. 2. Target vaccinations to those with the lowest number of unvaccinated connections. 3. Randomly vaccinate. We discovered that strategy 1 was significantly more effective than strategy 2 for Power Law (31% fewer people infected) but not for Binomial (7% fewer). Thus we conclude that before an optimized strategy for distributing a limited supply of vaccines can be designed, the degree distribution of the actual population must be investigated.

Location

DeRosa University Center, Ballroom

Start Date

20-4-2013 10:00 AM

End Date

20-4-2013 12:00 PM

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COinS

Apr 20th, 10:00 AM Apr 20th, 12:00 PM

Pandemic at Pacific

DeRosa University Center, Ballroom

The classic SIR model for disease spread utilizes a system of ODE'S that assume a population is well mixed and displays some homogenous behavior. In this project we investigate how accurate this assumption is by comparison with a more realistic Network Model for disease spread. For the Network Model we came up with four different possible degree distributions: Uniform, Power Law, Binomial, and Bimodal Binomial. We found that the ODE model severely overestimates both the size of the outbreak and its duration. The difference between the 4 distributions was not as large as the ODE model; the largest difference was a 20% higher number of total infected in the Binomial versus the Power Law distribution. Next, we investigated the effect of a limited amount of vaccinations on different networks (specifically Binomial and Power Law). We proposed 3 possible vaccination strategies: 1. Target vaccinations to those with the highest number of unvaccinated connections. 2. Target vaccinations to those with the lowest number of unvaccinated connections. 3. Randomly vaccinate. We discovered that strategy 1 was significantly more effective than strategy 2 for Power Law (31% fewer people infected) but not for Binomial (7% fewer). Thus we conclude that before an optimized strategy for distributing a limited supply of vaccines can be designed, the degree distribution of the actual population must be investigated.