Sequential Monte Carlo - EM algorithm for Disease Transmission Models

Estimating the parameters of disease transmission models is an important component in analyzing disease outbreaks and inferring transmission networks. The introduction of genetic data into disease transmission models has enabled more detailed inference, particularly through phylogenetic trees derived from the genetic data. Existing approaches often rely on a single phylogenetic tree to subset transmission trees from a set of possible transmission trees inferred from epidemiological data. However, such methods typically do not account for the uncertainty inherent in phylogenetic reconstruction. This thesis introduces a Sequential Monte Carlo-Expectation Maximization (SMC-EM) framework that explicitly incorporates uncertainty in transmission and phylogenetic trees. We treat these trees as latent variables and use observed genetic sequences, sampling times, and epidemiological data to inform the model. Our method constructs transmission and phylogenetic trees sequentially, conditioned on infection times, and updates parameter estimates iteratively via a variant of the EM algorithm. We evaluate the performance of the proposed method through extensive simulation studies and demonstrate its applicability using a real-world outbreak dataset. The results indicate that the SMC-EM approach provides improved parameter estimates while effectively capturing the uncertainty in latent tree structures. 

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