Integrated Pest Management with Stochastic Birth Rate for Prey Species

Frontiers in Neuroscience

Timothy eComar¹  Daniel eHrozencik²  Olcay eAkman³ 

[1] Benedictine University;Chicago State University;Illinois State University;

关键词: stability;    environment;    eradication;    predator-prey interactions;    permanent suppression;   

DOI  :  10.3389/fnins.2013.00141

来源: DOAJ

【 摘 要 】

X. Song and Z. Xiang [5] 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 impulsiveperiod for which a globally asymptotically stable pest-eradication periodic solution exists, as well asconditions on the impulsive period for which the prey species is permanently maintained under aneconomically acceptable threshold. We extend their model by including stage structure for both predatorand prey as well as by adding stochastic elements in the birth rate of the prey. As in [5], we find theconditions under which a globally asymptotically stable pest eradication periodic solution exists. Inaddition, we numerically show the relationship between the stochastically varying birth rate of the preyand the necessary efficacy of the pesticide for which the probability of eradication of the prey speciesis above 90%. This is significant because the model recognizes varying environmental and climaticconditions which affect the resources needed for pest eradication.

【 授权许可】

Unknown