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.