Bifurcation and global stability in an eco-epidemic model with refuge
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In this work, we formulate a predator–prey–pathogen model in which the predator is specialist in nature and infected prey can undergo refugia of constant size to avoid predator attack. To investigate the predation effect on the epidemics, we take a situation where the predator eats infected prey only. This is in accordance with the fact that the infected individuals are less active and can be caught more easily. Though it is a well-known fact that consumption of infected prey may harm predator population, the opposite holds in few cases. This leads to a controlled measure of disease prevalence. As predator consumes a particular type of prey species, Holling type II functional response is appropriate. This corroborates to the specialist type of predator. For biological validity of the model, boundedness of the system is studied. The dynamical behavior of the model has been analyzed throughly. Model analysis shows that all the population remains in coexistence when predator consumes the infected prey rather than the susceptible one. The results establish the fact that the effects of refuge used by prey decrease the equilibrium density of susceptible prey population, whereas the opposite holds for infected prey population. However, equilibrium density of predator may decrease or increase by increasing the amount of prey refuge. Global stability of the coexistence equilibrium point is developed by using Li and Muldowney’s high-dimensional Bendixson’s criterion. Numerical simulations are performed to validate our theoretical results.
KeywordsEco-epidemic model Prey refuge Global stability Hopf bifurcation Persistence
The authors are grateful to the editor and anonymous reviewers for their helpful comments and suggestions for improving the paper.
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Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
- Haque M, Venturino E (2009) Modelling disease spreading in symbiotic communities, wildlife destruction, conservation and biodiversity. Nova Science Publishers, New YorkGoogle Scholar
- Holmes JC, Bethal WM (1972) Modifications of intermediate host behavior by parasites. In: Canning EV, Wright CA (eds) Behavioural aspects of parasite transmission. Suppl I to Zool. f Linnean Soc vol 51, pp 123–149Google Scholar
- Hoy MA (1985) Almonds (California). In: Helle W, Sabelis MW (eds) Spider mites: their biology, natural enemies and control, World Crop Pests, vol 1B. Elesvier, Amsterdam, pp 229–310Google Scholar
- Kabata Z (1985) Parasites and disease of fish cultured in the tropics. Taylor and Francis, LondonGoogle Scholar
- Moore J (2002) Parasites and the behaviour of animals. Oxford University Press, OxfordGoogle Scholar
- Pal AK, Samanta GP (2013) A ratio-dependent eco-epidemiological model incorporating a prey refuge. Univ J Appl Math 1(2):86–100Google Scholar
- Van Dobben WH (1952) Sublethal effects of three ectoparasites on fish. J Fish Biol 7:283–294Google Scholar