Stochastic Trojan Y-chromosome models for eradication of invasive fish
October 6, 2011
2:30 p.m.
Xueying Wang
Abstract
A wide variety of exotic aquatic species, which were introduced and established as a result of human activities in the US, inflict enormous damage, which has resulted in the annual economic loss of billions of dollars (Pimentel et al., 2005). Gutierrez and Teem (2006) proposed a Trojan Y-chromosome eradication strategy for an invasive fish species. Pashad and Gutierrez (2010) proved the existence of a global attractor for the system derived by Gutierrez and Teem (2006) with the inclusion of spatial spread of the fish population. Their results reveal the extinction of an invasive fish species is always possible as time goes to infinity. However, this is not practical. It hence motivates our work on stochastic models. We develop two stochastic models, one that is based solely on the birth and death of fish species, and the other that also incorporate migration of the fish population. In this presentation, I will talk about finite-time extinction and the recovery of an invasive fish species for the former model. This is a joint work with Jay Walton, Rana D. Pashad (KAUST) and Katie Storey (Carleton College).