Date of this Version
Podariu A., Jin Y.. The Effects of Biocontrol and Dispersal on the Dynamics of a Two-Stage Pest Population. Undergraduate Honors Thesis. University of Nebraska-Lincoln. 2022.
In this paper we consider two predator-prey models with a two-staged pest (prey) and its biocontroller (predator). In one model, the predator only eats the immature pest, while in the other the predator only eats the mature pest. We discuss the existence and global stability of the equilibria of these models. Each model had a trivial and a positive equilibrium, one of which must be globally asymptotically stable. Then we consider dispersal of both the pest and its biocontroller between two patches. We find that the pop- ulation dispersal may significantly change the dynamics of the populations in the sense that oscillation behaviors may occur in the two-patch model for certain dispersal rates. In particular, we find that the dispersal rates of the mature prey in the first and second patches affect whether the population densities converge to an equilibrium or oscillate.