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PhyDyn: Epidemiological modelling in BEAST2

PhyDyn is a BEAST2 package for performing Bayesian phylogenetic inference under models that deal with structured populations with complex population dynamics. This package enables simultaneous estimation of epidemiological parameters and pathogen phylogenies. The package implements a coalescent model for a large class of epidemic processes specified by a deterministic nonlinear dynamical system. Genealogies are specified as timed phylogenetic trees in which lineages are associated with the distinct subpopulation in which they are sampled. Epidemic models are defined by a series of ordinary differential equations (ODEs) specifying the rates that new lineages introduced in the population (birth matrix) and the rates at which migrations, or transition between states occur (migration matrix). The ODE syntax allows the user to define and use complex mathematical expressions such as polynomials and trigonometric functions. Currently, PhyDyn works with deterministic demographic models. Future versions may incorporate other population models, methods for simulating trees conditional on an epidemic process and include semiparametric epidemiological models.

Overview

PhyDyn implements a structured coalescent model [1] for a large class of epidemic processes specified by a deterministic nonlinear dynamical system. Genealogies are specified as timed phylogenetic trees in which lineages are associated with the distinct subpopulation in which they are sampled. Epidemic models are defined by a series of ordinary differential equations (ODEs) specifying the rates that new lineages introduced in the population (birth matrix F) and the rates at which migrations, or transition between states occur (migration matrix G). The package computes:

• Population trajectory: a time series of population sizes and rate matrices (F,G) generated by solving the ODEs that define the epidemic model.
• The state probabilities and coalescent rates along the tree intervals. In particular, the package computes these values at branching points e.g. the root. State probabilities are calculated by solving a set of ODEs along the tree intervals backwards in time.
• Tree log-likelihood: calculated as the sum of the probabilities of the occurrence of the coalescent events at the branching points, and the probabilities that no coalescence occurs along the branches i.e. between sampling and coalescence events. In the general case, the latter is computed within the same of set of ODEs used to calculate state probabilities.

PhyDyn provides XML-ready classes for the specification of complex population models, generation of structured tree intervals and calculation of the log-likelihood of a structured dated tree conditional on a complex demographic history.

This Wiki provides information on PhyDyn's:

• Population Model
• Structured Tree Likelihood
• Loggers
• Examples: Ebola and Influenza.

References

• [1] Volz EM, 2012, Complex population dynamics and the coalescent under neutrality, Genetics, Vol:190, ISSN:0016-6731, Pages:187-201.
• [2] Erik Volz and Igor Siveroni, 2018, Bayesian phylodynamic inference with complex models [PLOS]. PLOS COMPUTATIONAL BIOLOGY, Vol: 14, ISSN: 1553-7358