Encounter Network and Its Application to Studying Epidemic Spread through Public Transportation Networks

Epidemic diseases have always been a challenging issue in public health. Densely populated urban public transportation systems could be the perfect candidate for transmitting epidemics by direct contact with the infected population and contaminated surfaces. In network analysis, betweenness centrality (BC), as the primary metric, has been used to measure an individual’s communication in the network. This research uses this concept to measure the risk of transmitting disease in public transportation links. For each network node, the set of shortest paths from that node to all other nodes compose a shortest paths sub-graph (tree). Source node total betweenness centrality (TBC) is defined as the sum of BC of all edges of this tree. Similarly, the shortest path sub-graph consisting of the set of the shortest paths from all nodes to a single target node is considered, and the target node TBC is defined as the sum of BC of all edges of this tree. The node encounter matrix is also defined to measure each node pair encounter in the network. The source node TBC of a node depicts the risk of transmitting the disease from that node to other nodes. Conversely, the target node TBC of a node is related to the risk of transmitting the disease from other nodes to that node. The susceptible-infected model is used to evaluate the proposed method by measuring the number of infected nodes.