Estimating thresholds for the contact process with permanent immunity on complex networks

We present an improvement in estimating the epidemic threshold for a modified susceptible-infected-removed model. We applied the pair heterogeneous mean-field theory on heterogeneous quenched networks. Our theoretical results are compared with extensive Monte Carlo simulations concerning the model dynamics on random regular and power-law networks. The epidemic thresholds obtained using pair heterogeneous mean-field theory agree with simulation results. We analyze the critical scaling of the model as well. At last, epidemic outbreaks emerge for infective probabilities above the critical threshold.