A model of predator-prey dynamics as modified by the action of a parasite. (English) Zbl 0698.92024

Summary: 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.


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
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