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- W3047977619 abstract "In this paper, we propose a stage-structured predator-prey model with migrations among patches in an <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>n</mml:mi></mml:math>-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> is established: the predator dies out if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math> while the predator persists if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math>. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:msub><mml:mrow><mml:mi mathvariant=normal>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>. 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." @default.
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- W3047977619 date "2020-08-08" @default.
- W3047977619 modified "2023-10-16" @default.
- W3047977619 title "A Stage-Structured Predator-Prey Model in a Patchy Environment" @default.
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- W3047977619 doi "https://doi.org/10.1155/2020/6028019" @default.
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