Early die out events in SIR epidemic models

Authors

Jonathan Ballone, Montclair State UniversityFollow

Abstract

We are interested in the behavior of an SIR epidemic model with respect to low-probability events. Specifically, we want to identify the probability of the early die out of a disease. Ordinary differential equations are commonly used to model SIR systems. However, this approach fails to describe the spontaneous die out event. We develop a Markov SIR model from which the probability of early die out can be captured. Additional simulations reveal that this model agrees closely with the ODE solutions when these low-probability events are ignored.

Author Bio

I will be graduating at the end of the 2009-2010 academic year with a major in Mathematics and minors in Computer Science and Anthropology. I plan to enroll in a PhD program for Mathematics in the Fall of 2010. This project has affirmed my interest in doing research, though my mathematical interests are still too broad to determine what field I will focus my graduate studies in. My long-term goal is to teach at the University level. My hobbies include ping-pong, poetry and playing the bass guitar.

Faculty Sponsor

Lora Billings

Recommended Citation

Ballone, Jonathan (2010) "Early die out events in SIR epidemic models," Rose-Hulman Undergraduate Mathematics Journal: Vol. 11: Iss. 1, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol11/iss1/3