The objective of this paper is to present a network-based optimization method for identifying links in an air traffic network responsible for carrying infected passengers into previously unexposed regions. The required data include individual infection reports (i.e., when the disease was first reported in a region), travel pattern data, and other geographic properties. The network structure is defined by nodes and links, which represent regions (cities, states, countries) and travel routes, respectively. The proposed methodology is novel in its attempt to replicate an outbreak pattern atop a transportation network by exploiting regional infection data. The problem parallels a related problem in phylodynamics, which uses genetic sequencing data to reconstruct the most likely spatiotemporal path of infection.