A hybrid parabolic and hyperbolic equation model for a population with separate dispersal and stationary stages: well-posedness and population persistence. (English) Zbl 1427.92074
Summary: In this paper, we develop a hybrid parabolic and hyperbolic equation model, in which a reaction-diffusion equation governs the random movement and settlement of dispersal individuals, while a first-order hyperbolic equation describes the growth of stationary individuals with age structure. We prove the existence and uniqueness of the solution of the model using the monotone method based on a comparison principle. We study the population persistence criteria in terms of four related measures. We numerically investigate how the interplay between population dispersal, reproduction, settlement, and habitat boundary affects the population persistence.
MSC:
| 92D25 | Population dynamics (general) |
| 35K57 | Reaction-diffusion equations |
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
hybrid model; comparison principle; existence-uniqueness; persistence; next generation operator; net reproductive rateReferences:
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