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We numerically study the phase diagram of a three-state host-parasite modelon the square lattice motivated by population biology. The model is anextension of the contact process, and the three states correspond to an emptysite, a host, and a parasite. We determine the phase diagram of the model byscaling analysis. In agreement with previous results, three phases areidentified: the phase in which both hosts and parasites are extinct (S_{0}),the phase in which hosts survive but parasites are extinct (S_{01}), and thephase in which both hosts and parasites survive (S_{012}). We argue that boththe S_{0}-S_{01} and S_{01}-S_{012} boundaries belong to the directedpercolation class. In this model, it has been suggested that an excessivelylarge reproduction rate of parasites paradoxically extinguishes hosts andparasites and results in S_{0}. We show that this paradoxical extinction is afinite size effect; the corresponding parameter region is likely to disappearin the limit of infinite system size.

Numerical study of a three-state host-parasite system on the square lattice