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