Construction of semi-Markov genetic-space-time SEIR models and inference

Identifying transmission links of an infectious disease through a host population is critical to understanding its epidemiology and informing measures for its control. Infected hosts close together in their locations and timings are often thought to be linked, but timing and locations alone are usually consistent with many different scenarios of who infected whom. To infer more reliably who-transmitted-to-whom over the course of a disease outbreak caused by a fast-evolving pathogen, pathogen genomic data have been combined with spatial and temporal data. However, the manner to combine these data remains today a modeling and statistical challenge. One of the approaches recently proposed is based on an extension of stochastic Susceptible-Exposed-Infectious-Removed (SEIR) models. In this article, we present this extension that combines (i) an individual-based, spatial, semi-Markov SEIR model for the spatio-temporal dynamics of the pathogen, and (ii) a Markovian evolutionary model for the temporal evolution of genetic sequences of the pathogen. The resulting model is a state-space model including latent vectors of high dimension. Then, we describe a new algorithm that allows an approximate Bayesian inference of model parameters and latent variables. Finally, the capacity of the estimation algorithm to reconstruct transmission trees (i.e. who infected whom) is assessed with a simulation study. We especially investigate how the inference method performs when only a fraction of pathogen genomic data is available.