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Dynamics of a predator-prey system with prey subject to Allee effects and disease
Dynamics of a predator-prey system with prey subject to Allee effects and disease
- Source :
- Mathematical Biosciences and Engineering, Vol 11, Iss 4, Pp 877-918 (2014)
- Publication Year :
- 2014
- Publisher :
- AIMS Press, 2014.
-
Abstract
- In this article, we propose a general predator-prey system where prey is subject to Allee effects and disease with the following unique features: (i) Allee effects built in the reproduction process of prey where infected prey (I-class) has no contribution; (ii) Consuming infected prey would contribute less or negatively to the growth rate of predator (P-class) in comparison to the consumption of susceptible prey (S-class). We provide basic dynamical properties for this general model and perform the detailed analysis on a concrete model (SIP-Allee Model) as well as its corresponding model in the absence of Allee effects (SIP-no-Allee Model); we obtain the complete dynamics of both models: (a) SIP-Allee Model may have only one attractor (extinction of all species), two attractors (bi-stability either induced by small values of reproduction number of both disease and predator or induced by competition exclusion), or three attractors (tri-stability); (b) SIP-no-Allee Model may have either one attractor (only S-class survives or the persistence of S and I-class or the persistence of S and P-class) or two attractors (bi-stability with the persistence of S and I-class or the persistence of S and P-class). One of the most interesting findings is that neither models can support the coexistence of all three S, I, P-class. This is caused by the assumption (ii), whose biological implications are that I and P-class are at exploitative competition for S-class whereas I-class cannot be superior and P-class cannot gain significantly from its consumption of I-class. In addition, the comparison study between the dynamics of SIP-Allee Model and SIP-no-Allee Model lead to the following conclusions: 1) In the presence of Allee effects, species are prone to extinction and initial condition plays an important role on the surviving of prey as well as its corresponding predator; 2) In the presence of Allee effects, disease may be able to save prey from the predation-driven extinction and leads to the coexistence of S and I-class while predator can not save the disease-driven extinction. All these findings may have potential applications in conservation biology.
Details
- Language :
- English
- ISSN :
- 15510018
- Volume :
- 11
- Issue :
- 4
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematical Biosciences and Engineering
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.219556b07ace4882b468bc3d8aa49a50
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/mbe.2014.11.877