title: Integrated pest management with stochastic birth rate for prey species.
abstract: Song and Xiang (2006) developed an impulsive differential equations model for a two-prey one-predator model with stage structure for the predator. They demonstrate the conditions on the impulsive period for which a globally asymptotically stable pest-eradication periodic solution exists, as well as conditions on the impulsive period for which the prey species is permanently maintained under an economically acceptable threshold. We extend their model by including stage structure for both predator and prey as well as by adding stochastic elements in the birth rate of the prey. As in Song and Xiang (2006), we find the conditions under which a globally asymptotically stable pest eradication periodic solution exists. In addition, we numerically show the relationship between the stochastically varying birth rate of the prey and the necessary efficacy of the pesticide for which the probability of eradication of the prey species is above 90%. This is significant because the model recognizes varying environmental and climatic conditions which affect the resources needed for pest eradication.
authors: Department of Mathematics, Illinois State University Normal, IL, USA.
authors: Olcay
authors: O
authors: Akman
authors: Timothy D
authors: TD
authors: Comar
authors: Daniel
authors: D
authors: Hrozencik
keywords: environment; eradication; permanent suppression; predator-prey interactions; stability
references: J Theor Biol. 2006 Oct 7;242(3):683-98
references: 16797031
references: J Math Biol. 2002 Feb;44(2):185-99
references: 11942532
references: Bull Math Biol. 2005 Jan;67(1):115-35
references: 15691542
references: J Evol Biol. 2009 Jun;22(6):1193-202
references: 19416415
references: J Theor Biol. 2011 Jul 7;280(1):108-16
references: 21477598
references: Math Med Biol. 2003 Dec;20(4):309-25
references: 14969382