A ratio-dependent predator-prey model with disease in the prey. (English) Zbl 1024.92017

Xiao, Yanni; Chen, Lansun

Appl. Math. Comput. 131, No. 2-3, 397-414 (2002).

In this paper the prey population is divided into susceptibles and infectives, where the infectives do not recover, and the predator is consuming only the infectives. The functional response is of ratio dependent Holling type. Conditions are established for non-persistence and for persistence of the system. Under some conditions on the parameters the system may possess a positive equilibrium and still some solutions may tend to the equilibria on the boundary. Also there are cases when some solutions tend to the equilibrium that represents the absence of infectives and predators, and some other solutions tend to the equilibrium that represents the absence of the predators only. The occurrence of a Hopf bifurcation is also established as the susceptible prey population of the positive equilibrium is increased.

Reviewer: Miklos Farkas (Budapest)

MSC:

92D25	Population dynamics (general)
34C60	Qualitative investigation and simulation of ordinary differential equation models

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