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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:

92D40 | Ecology |

92D30 | Epidemiology |

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

65C60 | Computational problems in statistics (MSC2010) |

37N25 | Dynamical systems in biology |

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\textit{K. p. Das} and \textit{J. Chattopadhyay}, Math. Methods Appl. Sci. 35, No. 6, 659--675 (2012; Zbl 1236.92059)

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