We analyse a general time-discrete mathematical model of host-parasite population dynamics with harvesting, in which the host can be regarded as a pest. We harvest a portion of the host population at a moment in each year. Our model involves the density effect on the host population. We investigate the condition in which the harvesting of the host results in a paradoxical increase of its equilibrium population size. Our results imply that for a family of pest-enemy systems, the paradox of pest control could be caused essentially by the interspecific relationship and the intraspecific density effect.
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