SharpTNI: Counting and Sampling Parsimonious Transmission Networks under a Weak Bottleneck

Background Technological advances in genomic sequencing are facilitating the reconstruction of transmission histories during outbreaks in the fight against infectious diseases. However, accurate disease transmission inference using this data is hindered by a number of challenges due to within-host pathogen diversity and weak transmission bottlenecks, where multiple genetically-distinct pathogenic strains co-transmit. Results We formulate a combinatorial optimization problem for transmission network inference under a weak bottleneck from a given timed phylogeny and establish hardness results. We present SharpTNI, a method to approximately count and almost uniformly sample from the solution space. Using simulated data, we show that SharpTNI accurately quantifies and uniformly samples from the solution space of parsimonious transmission networks, scaling to large datasets. We demonstrate that SharpTNI identifies co-transmissions during the 2014 Ebola outbreak that are corroborated by epidemiological information collected by previous studies. Conclusions Accounting for weak transmission bottlenecks is crucial for accurate inference of transmission histories during outbreaks. SharpTNI is a parsimony-based method to reconstruct transmission networks for diseases with long incubation times and large inocula given timed phylogenies. The model and theoretical work of this paper pave the way for novel maximum likelihood methods to co-estimate timed phylogenies and transmission networks under a weak bottleneck.