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Role of environmental disturbance in an eco-epidemiological model with disease from external source. (English) Zbl 1236.92059
Summary: An eco-epidemiological model with random environmental disturbance is proposed and analyzed. We assume that the susceptible prey population can acquire infection both from external sources and from internal transmission of the disease. It is also assumed that there is no recovery of the disease, and the consumption of diseased prey has a deleterious effect on the predator population. Conditions for the extinction of the predator and the prey populations are worked out. The most important observation of the present investigation is that oscillatory behavior of the populations observed in deterministic framework undergoes stable coexistence in the stochastic framework.
MSC:
92D40Ecology
92D30Epidemiology
34C60Qualitative investigation and simulation of models (ODE)
60H10Stochastic ordinary differential equations
65C60Computational problems in statistics
37N25Dynamical systems in biology