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

We numerically study the phase diagram of a three-state host-parasite model on the square lattice motivated by population biology. The model is an extension of the contact process, and the three states correspond to an empty site, a host, and a parasite. We determine the phase diagram of the model by scaling analysis. In agreement with previous results, three phases are identified: 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 the phase in which both hosts and parasites survive (S_{012}). We argue that both the S_{0}-S_{01} and S_{01}-S_{012} boundaries belong to the directed percolation class. In this model, it has been suggested that an excessively large reproduction rate of parasites paradoxically extinguishes hosts and parasites and results in S_{0}. We show that this paradoxical extinction is a finite size effect; the corresponding parameter region is likely to disappear in the limit of infinite system size.