When running the simulations, we find that the infection rate q must be greater than a certain minimum value q min for the epidemics to be self-sustaining and cover a large fraction of the network. We also observe that q min depends on the network's average degree ,k.. A less-connected network with smaller average degree ,k. requires a larger value of q min to sustain an epidemic, as compared to a more highly-connected network with higher ,k.. Hence, we fine tune the infection probability q so that 50%-70% of the nodes are infected in one epidemic simulation. We find that q min < 0.80 in the case of ,k. = 3, q min < 0.20 for ,k. = 10, and q min < 0.08 for ,k. = 20. Finally, we note that while it is relatively easy to infect the majority of the nodes in the network with high ,k., infecting all nodes is extremely hard. We need q to be very close to one before the epidemic infects the entire network.