Integrated Pest Management with Stochastic Birth Rate for Prey Species
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 a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2013-08-01
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| Series: | Frontiers in Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fnins.2013.00141/full |
| _version_ | 1828198950066192384 |
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| author | Olcay eAkman Timothy eComar Daniel eHrozencik |
| author_facet | Olcay eAkman Timothy eComar Daniel eHrozencik |
| author_sort | Olcay eAkman |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T10:46:53Z |
| format | Article |
| id | doaj.art-aea486a7cace419995620a5803ce1c63 |
| institution | Directory Open Access Journal |
| issn | 1662-453X |
| language | English |
| last_indexed | 2024-04-12T10:46:53Z |
| publishDate | 2013-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Neuroscience |
| spelling | doaj.art-aea486a7cace419995620a5803ce1c632022-12-22T03:36:24ZengFrontiers Media S.A.Frontiers in Neuroscience1662-453X2013-08-01710.3389/fnins.2013.0014153773Integrated Pest Management with Stochastic Birth Rate for Prey SpeciesOlcay eAkman0Timothy eComar1Daniel eHrozencik2Illinois State UniversityBenedictine UniversityChicago State UniversityX. 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.http://journal.frontiersin.org/Journal/10.3389/fnins.2013.00141/fullstabilityenvironmenteradicationpredator-prey interactionspermanent suppression |
| spellingShingle | Olcay eAkman Timothy eComar Daniel eHrozencik Integrated Pest Management with Stochastic Birth Rate for Prey Species Frontiers in Neuroscience stability environment eradication predator-prey interactions permanent suppression |
| title | Integrated Pest Management with Stochastic Birth Rate for Prey Species |
| title_full | Integrated Pest Management with Stochastic Birth Rate for Prey Species |
| title_fullStr | Integrated Pest Management with Stochastic Birth Rate for Prey Species |
| title_full_unstemmed | Integrated Pest Management with Stochastic Birth Rate for Prey Species |
| title_short | Integrated Pest Management with Stochastic Birth Rate for Prey Species |
| title_sort | integrated pest management with stochastic birth rate for prey species |
| topic | stability environment eradication predator-prey interactions permanent suppression |
| url | http://journal.frontiersin.org/Journal/10.3389/fnins.2013.00141/full |
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