A model of predator-prey dynamics as modified by the action of a parasite.

*(English)*Zbl 0698.92024Summary: A predator-prey population is described in which the prey population may be either a secondary host or a primary host to a parasite, but the predator is always a primary host. Those prey that have been invaded by the parasite have their behavior modified so as to make them more susceptible to predation. The model is described by a system of three autonomous ordinary differential equations. Conditions for persistence of all populations are given in the case that both populations are primary hosts. A brief discussion of the stability of the interior equilibrium is given.

##### MSC:

92D25 | Population dynamics (general) |

37N99 | Applications of dynamical systems |

34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |

34D99 | Stability theory for ordinary differential equations |

37C75 | Stability theory for smooth dynamical systems |

37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |

##### Keywords:

extinction; predator-prey population; system of three autonomous ordinary differential equations; Conditions for persistence; primary hosts; stability of the interior equilibrium
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\textit{H. I. Freedman}, Math. Biosci. 99, No. 2, 143--155 (1990; Zbl 0698.92024)

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##### References:

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