significantly from that under the SI model. The differences are summarized below.

-   The set of possible sources in the SI model [@ShaZam_10; @ShaZam_11; @ShaZam_12] is restricted to the set of infected nodes. In the SIR model, all nodes are possible information sources because we assume susceptible nodes and recovered nodes are indistinguishable and a healthy node may be a recovered node so can be the information source. Therefore, the number of candidate sources is much larger in the SIR model than that in the SI model.

-   A key observation in [@ShaZam_10; @ShaZam_11; @ShaZam_12] is that on regular trees, all permitted permutations of infection sequences (a infection sequence specifies the order at which nodes are infected) are equally likely under the SI model. The number of possible permutations from a fixed root node, therefore, decides the likelihood of the root node being the source. However, under the SIR model, different infection sequences are associated with different probabilities, so counting the number of permutations are not sufficient.

-   [@ShaZam_10; @ShaZam_11; @ShaZam_12] proved that the node with the maximum closeness centrality is the an MLE on regular-trees. We define the infection closeness centrality to be the inverse of the sum of 