Table 3.

Modeling of unobserved processes in the sequential phylogenetic family. For the sequence mutation process, NA stands for not applicable. 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. In the inference method, we mention how phylogenetic trees are used to infer transmission trees (either internal nodes or branches are labelled with the host or phylogenetic trees are used as a source of information). * means multiple sequences can be considered per epidemiological unit.

Method (Name) [Reference]	Sequence Mutation	Within-Host Evolution	Transmission	Case Observation	Inference Method
Cottam et al., 2008 [2]	NA	No explicit model	SEIR (latency/infectious period)	All cases are observed and sampled	Label internal nodes
		Complete	Random mixing		Maximum Likelihood
			Single
Didelot et al., 2014 [17]	NA	Coalescent process	SIR (infectious period)	All cases are observed and sampled	Label branches
		Complete	Random mixing		Bayesian
			Single
Eldholm et al., 2016 [39]	NA	Coalescent process	SEIR (latency/infectious period)	Probability threshold	Information source
		Complete	Random mixing		Edmonds’ algorithm
			Single
Didelot et al., 2017 (Transphylo) [40]	NA	Coalescent process	SI (generation times)	Proportion of sampled cases	Label branches
		Complete	Random mixing		Bayesian
			Single
Sashittal et al., 2020 (TiTUS) [31]	NA	No explicit model	No explicit model	All cases are observed and sampled	Label internal nodes
		Weak *			Logical problem