Yahani Wathsala: Simulation based analysis of infectious disease transmission trees

Abstract: In this thesis, we investigate how different stochastic transmission models and superspreader behavior are reflected in transmission trees. As our models of interest we use four continuous-time Markov chain epidemics in a closed population, a homogeneous SIR model, an SEIR model with a latent period, an SIR model with Gamma-distributed individual infectivity to capture superspreading, and an SIR model with households and global mixing. Drawing inspiration from tree-based epidemic analysis, we simulate each model using the Gillespie algorithm and record who infected whom, constructing a transmission tree for every outbreak.

In our simulations, the superspreading model produces highly overdispersed offspring distributions, large Gini coefficients and strong ”top x% cause y%” effects, with many infections generated by a small number of high degree nodes. The household model yields comparatively shallow trees, similar in depth to the superspreading model despite arising from a very different mechanism. We also examine backward, ancestral offspring statistics and show that ancestors tend to have more offspring than a typical infectious individual, consistent with size biased sampling. As a further assessment of the models, we compare tree-based statistics with final epidemic sizes. Based on these results, we argue that forward and backward transmission summaries can help to identify the superspreading and mixing structure and to guide the selection of simple stochastic models for real transmission-tree data.