Table 2.

Modeling of unobserved processes in the non-phylogenetic family. Within-host evolution (modeled or not) includes whether the transmission bottleneck is complete or weak. When transmission is modeled, we mention the states hosts can find themselves in (S: susceptible, E: latent, I: infectious, R: removed). In addition, either geographical distance (spatial kernel), contact data, or random mixing are considered. Finally, the transmission model mentions whether there is only one index case possible (single introduction) or multiple.

Method (Name) [Reference]	Sequence Mutation	Within-Host Evolution	Transmission	Case Observation	Inference Method
Aldrin et al., 2011 [28]	Kimura model	No explicit model	SIR (infectious period)	All cases are observed but not always sampled	Partial Maximum Likelihood
		Complete	Distance kernel
			Multiple
Jombart et al., 2011 (Seqtrack) [16]	User’s choice	No explicit model	No explicit model	All cases are observed and sampled	Edmonds algorithm
		Complete
Ypma et al., 2012 [32]	Deletion + Transition + Transversion	No explicit model	SEIR (latency/infectious period)	All cases are observed but not always sampled	Bayesian
		Complete	Spatial kernel
			Single
Jombart et al., 2014 (outbreaker) [24]	Mutation rate	No explicit model	SI (generation times)	Proportion of sampled cases	Bayesian
		Complete	Random mixing
			Multiple
Worby et al., 2014 [37]	Mutation rate	Pathogen population size	No explicit model	All cases are observed and sampled	Observed genetic distance vs. theoretical distribution
		Weak
Famulare et al., 2015 [38]	Mutation rate	No explicit model	No explicit model	No assumption	Likelihood ratio test + Pruning algorithm
Worby et al., 2016 (bitrugs) [6]	No explicit model	No explicit model	SEIR (latency/infectious period)	Test sensitivity < 1	Bayesian
		No assumption	Random mixing
			Multiple
Campbell et al., 2019 (outbreaker2) [30]	Mutation rate	No explicit model	SI (generation times)	Proportion of sampled cases	Bayesian
		Complete	Contact data
			Multiple