Stochastic spatial structured model for vertically and horizontally transmitted infection

We study a space structured stochastic model for vertical and horizontal transmitted infection. By means of simple and pair mean-field approximation as well as Monte Carlo simulations, we construct the phase diagram, which displays four states: healthy (H), infected (I), extinct (E), and coexistent (C). In state H only healthy hosts are present, whereas in state I only infected hosts are present. The state E is characterized by the extinction of the hosts whereas in state C there is a coexistence of infected and healthy hosts. In addition to the usual scenario with continuous transition between the I, C and H phases, we found a different scenario with the suppression of the C phase and a discontinuous phase transition between I and H phases.