Rare Events in Stochastic Population Models
Garrett Nieddu, Montclair State University
Noise can play a critical role in a wide array of physical and biological dynamical systems. The noise may be internal or external to the system. Internal noise is intrinsic to the system itself, and in stochastic population models, arises due to the random interactions of discrete agents in the system. On the other hand, external noise arises from a source outside of the system. There are a number of situations where noise can induce a large fluctuation that leads to population extinction, switching between metastable states in ecological systems, or the escape of a particle from a potential well.
In this presentation, I will describe how to formulate the master equation that completely describes the stochastic dynamics of population models where the noise is internal to the system. I will discuss how both numerical methods and analytical methods may be used to investigate stochastic population dynamics, including how WKB theory can be used to understand the rare, noise-induced transitions. To demonstrate the power of the methodology, I will discuss two different systems to which the methods have been applied. In the first system, the extinction dynamics of an isolated bi-stable population is investigated. In the second system, the outbreak vulnerability and extinction dynamics for a stochastic Ebola virus disease model is studied.