A Stage-Structured Predator-Prey Model in a Patchy Environment
In this paper, we propose a stage-structured predator-prey model with migrations among patches in an n-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, ℛ0. Inequalities describing the relationship...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6028019 |
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| author | Xuejuan Lu Yuming Chen Shengqiang Liu |
| author_facet | Xuejuan Lu Yuming Chen Shengqiang Liu |
| author_sort | Xuejuan Lu |
| collection | DOAJ |
| description | In this paper, we propose a stage-structured predator-prey model with migrations among patches in an n-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, ℛ0. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by ℛ0 is established: the predator dies out if ℛ0<1 while the predator persists if ℛ0>1. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number ℛ0. By numerical simulations, we find that the dispersal may be a good thing or a bad thing because the dispersal could make the predator population thrive or extinct, and hence we might seek steady state in the ecological environment by controlling parameters related to the prey and the predator. |
| format | Article |
| id | doaj-art-28568036e8e548eba40d216182a86da3 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-28568036e8e548eba40d216182a86da32025-02-03T06:05:41ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/60280196028019A Stage-Structured Predator-Prey Model in a Patchy EnvironmentXuejuan Lu0Yuming Chen1Shengqiang Liu2College of Science, Qiqihar University, Qiqihar, Heilongjiang 161006, ChinaDepartment of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, CanadaSchool of Mathematical Sciences, Tiangong University, Tianjin 300387, ChinaIn this paper, we propose a stage-structured predator-prey model with migrations among patches in an n-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, ℛ0. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by ℛ0 is established: the predator dies out if ℛ0<1 while the predator persists if ℛ0>1. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number ℛ0. By numerical simulations, we find that the dispersal may be a good thing or a bad thing because the dispersal could make the predator population thrive or extinct, and hence we might seek steady state in the ecological environment by controlling parameters related to the prey and the predator.http://dx.doi.org/10.1155/2020/6028019 |
| spellingShingle | Xuejuan Lu Yuming Chen Shengqiang Liu A Stage-Structured Predator-Prey Model in a Patchy Environment Complexity |
| title | A Stage-Structured Predator-Prey Model in a Patchy Environment |
| title_full | A Stage-Structured Predator-Prey Model in a Patchy Environment |
| title_fullStr | A Stage-Structured Predator-Prey Model in a Patchy Environment |
| title_full_unstemmed | A Stage-Structured Predator-Prey Model in a Patchy Environment |
| title_short | A Stage-Structured Predator-Prey Model in a Patchy Environment |
| title_sort | stage structured predator prey model in a patchy environment |
| url | http://dx.doi.org/10.1155/2020/6028019 |
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