Reconstructing contact network parameters from viral phylogenies

Models of the spread of disease in a population often make the simplifying assumption that the population is homogeneously mixed, or is divided into homogeneously mixed compartments. However, human populations have complex structures formed by social contacts, which can have a significant influence on the rate of epidemic spread. Contact network models capture this structure by explicitly representing each contact which could possibly lead to a transmission. We developed a method based on kernel approximate Bayesian computation (kernel-ABC) for estimating structural parameters of the contact network underlying an observed viral phylogeny. The method combines adaptive sequential Monte Carlo for ABC, Gillespie simulation for propagating epidemics though networks, and a kernel-based tree similarity score. We used the method to fit the Barabasi-Albert network model to simulated transmission trees, and also applied it to viral phylogenies estimated from five published HIV sequence datasets. On simulated data, we found that the preferential attachment power and the number of infected nodes in the network can often be accurately estimated. On the other hand, the mean degree of the network, as well as the total number of nodes, were not estimable with kernel-ABC. We observed substantial heterogeneity in the parameter estimates on real datasets, with point estimates for the preferential attachment power ranging from 0.06 to 1.05. These results underscore the importance of considering contact structures when performing phylodynamic inference. Our method offers the potential to quantitatively investigate the contact network structure underlying viral epidemics.