Predator-Prey Dynamics with Disease in the Prey
The Holling-Tanner model for predator-prey systems is adapted to incorporatethe spread of disease in the prey. The analysis of the dynamics centers onbifurcation diagrams in which the disease transmission rate is the primaryparameter. The ecologically reasonable assumption that the diseased preyar...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.703 |
| _version_ | 1826859267067478016 |
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| author | Peter A. Braza |
| author_facet | Peter A. Braza |
| author_sort | Peter A. Braza |
| collection | DOAJ |
| description | The Holling-Tanner model for predator-prey systems is adapted to incorporatethe spread of disease in the prey. The analysis of the dynamics centers onbifurcation diagrams in which the disease transmission rate is the primaryparameter. The ecologically reasonable assumption that the diseased preyare easier to catch enables tractable analytic results to be obtained forthe stability of the steady states and the locations of Hopf bifurcationpoints as a function of the ecological parameters. Two parameters ofparticular relevance are the ratio of the predator's intrinsic growth rateto the prey's growth rate and the maximum number of infected prey that canbe eaten per time. The dynamics are shown to be qualitatively differentdepending on the comparative size of these parameters. Numerical resultsobtained with AUTO are used to extend the local analysis and furtherillustrate the rich dynamics. |
| first_indexed | 2025-02-16T19:16:27Z |
| format | Article |
| id | doaj.art-62ce0d1da4ef440baf985d18cca89a2a |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2025-02-16T19:16:27Z |
| publishDate | 2005-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-62ce0d1da4ef440baf985d18cca89a2a2025-01-24T01:49:46ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-09-012470371710.3934/mbe.2005.2.703Predator-Prey Dynamics with Disease in the PreyPeter A. Braza0Department of Mathematics and Statistics, University of North Florida, 4567 St. Johns Bluff Road, Jacksonville, FL 32224The Holling-Tanner model for predator-prey systems is adapted to incorporatethe spread of disease in the prey. The analysis of the dynamics centers onbifurcation diagrams in which the disease transmission rate is the primaryparameter. The ecologically reasonable assumption that the diseased preyare easier to catch enables tractable analytic results to be obtained forthe stability of the steady states and the locations of Hopf bifurcationpoints as a function of the ecological parameters. Two parameters ofparticular relevance are the ratio of the predator's intrinsic growth rateto the prey's growth rate and the maximum number of infected prey that canbe eaten per time. The dynamics are shown to be qualitatively differentdepending on the comparative size of these parameters. Numerical resultsobtained with AUTO are used to extend the local analysis and furtherillustrate the rich dynamics.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.703predator-preyhopf bifurcations.holling-tanner |
| spellingShingle | Peter A. Braza Predator-Prey Dynamics with Disease in the Prey Mathematical Biosciences and Engineering predator-prey hopf bifurcations. holling-tanner |
| title | Predator-Prey Dynamics with Disease in the Prey |
| title_full | Predator-Prey Dynamics with Disease in the Prey |
| title_fullStr | Predator-Prey Dynamics with Disease in the Prey |
| title_full_unstemmed | Predator-Prey Dynamics with Disease in the Prey |
| title_short | Predator-Prey Dynamics with Disease in the Prey |
| title_sort | predator prey dynamics with disease in the prey |
| topic | predator-prey hopf bifurcations. holling-tanner |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.703 |
| work_keys_str_mv | AT peterabraza predatorpreydynamicswithdiseaseintheprey |