Epidemiological inference from pathogen genomes: A review of phylodynamic models and applications

Abstract

Phylodynamics requires an interdisciplinary understanding of phylogenetics, epidemiology, and statistical inference. It has also experienced more intense application than ever before amid the SARS-CoV-2 pandemic. In light of this, we present a review of phylodynamic models beginning with foundational models and assumptions. Our target audience is public health researchers, epidemiologists, and biologists seeking a working knowledge of the links between epidemiology, evolutionary models, and resulting epidemiological inference. We discuss the assumptions linking evolutionary models of pathogen population size to epidemiological models of the infected population size. We then describe statistical inference for phylodynamic models and list how output parameters can be rearranged for epidemiological interpretation. We go on to cover more sophisticated models and finish by highlighting future directions.

Keywords: birth-death model; coalescent model; epidemiological models; phylodynamics.

Figure 1.

Representations of the key assumptions in standard phylodynamic analysis. (A) It is assumed that the underlying epidemic is growing exponentially and number of samples by extension. This corresponds to a constant rate of transmission (λ) per infected alongside constant rates of sampling infections and terminating infections (ψ and μ, respectively). (B) The transmission network is assumed to grow according to these parameters. Blue nodes correspond to sampled sequences and red nodes correspond to undiscovered or extinct infections. Node A is the first case. (C) It is assumed that the network in (B) corresponds to an underlying phylogeny of the pathogen where transmission co-occurs with branching. (D) An estimated phylogeny from sampled sequences. Phylodynamics uses the sample tree as a means of estimating the parameters driving (A) and (B).

Figure 2.

(A) Example stochastic trajectories in the infected compartment and sequenced subset of it. Stochastic exponential growth is accommodated by the constant rate birth–death. (B) An example of the deterministic exponential growth curve in the infected compartment as assumed by the coalescent exponential. (C) Sampling times present a source of information under the birth–death. (D) Coalescent events provide information in the coalescent while conditioning on sampling times.

Figure 3.

D refers to the duration of infection and T refers to the posterior tree height. (A) A flowchart of assumptions, methods, and inference under the constant rate birth–death. (B) As in (A) but with respect to the coalescent exponential.