Diffusive Epidemiological Predator–Prey Models with Ratio-Dependent Functional Responses and Nonlinear Incidence Rate

In this paper, when the predator breeds only by the prey, the relationship among the two classes of prey (susceptible and infected prey) and the predator is represented by using an epidemic model with nonlinear incidence and the response function depending on the density of the three individuals und...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2022, Vol.28 (1), p.43-57
Main Authors: Kim, Kwangjoong, Choi, Wonhyung, Ahn, Inkyung
Format: Article
Language:English
Subjects:
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Control
Dirichlet problem
Dynamical Systems
Dynamical Systems and Ergodic Theory
Ecological effects
Mathematics
Mathematics and Statistics
Predators
Response functions
Systems Theory
Vibration
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Summary:In this paper, when the predator breeds only by the prey, the relationship among the two classes of prey (susceptible and infected prey) and the predator is represented by using an epidemic model with nonlinear incidence and the response function depending on the density of the three individuals under homogeneous Dirichlet boundary conditions describing a hostile environment at its boundary. For this model, the coexistence steady state of three interacting species is mainly investigated, and the global stabilities of the extinction of all species and the survival of only healthy prey are discussed. Additionally, the conditions of the non-coexistence of three species are established. Finally, an ecological interpretation is also presented based on the results.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-020-09512-3