The value Θ = 0 is always a solution. In order to have a nonzero solution, the condition below which the epidemic dies out, and above which there is an endemic state. In Fig. 2, a comparison between the theoretical prediction
and the numerical observations is presented. Here, we have explicitly calculated the algorithmic betweenness for the greedy
routing as it only coincides with the topological betweenness for shortest-paths routing. The obtained curve separates two regions: an absorbing phase in which the epidemic disappears and an active phase where the infection is endemic