Bayesian methods to infer direct transmission using data from outbreaks in households

The study of how transmissible an infectious pathogen is and what its main routes of transmission are is key towards management and control of its spread. Some infections which begin with zoonotic or common-source transmission may additionally exhibit potential for direct person-to-person transmission. Methods to discern multiple transmission routes from observed outbreak datasets are thus essential. Features such as partial observation of the outbreak can make such inferences more challenging. This thesis presents a stochastic modelling framework to infer person-to-person transmission using data observed from a completed outbreak in a population of households. The model is specified hierarchically for the processes of transmission and observation. The transmission model specifies the process of acquiring infection from either the environment or infectious household members. This model is governed by two parameters, one for each source of transmission. While in continuous time they are characterised by transmission hazards, in discrete time they are characterised by escape probabilities. The observation model specifies the process of observation of outbreak based on symptom times and serological test results. The observation design is extended to address an ongoing outbreak with censored observation as well as to case-ascertained sampling where households are sampled based on index cases. The model and observation settings are motivated by the typical data from Hepatitis A virus (HAV) outbreaks. Partial observation of the infectious process is due to unobserved infection times, presence of asymptomatic infections and not-fully- sensitive serological test results. Individual-level latent variables are introduced in order to account for partial observation of the process. A data augmented Markov chain Monte Carlo (DA-MCMC) algorithm to estimate the transmission parameters by simultaneously sampling the latent variables is developed. A model comparison using deviance-information criteria (DIC) is formulated to test the presence of direct transmission, which is the primary aim in this thesis. In calculating DIC, the required computations utilise the DA-MCMC algorithm developed for the estimation procedures. \\ The inference methods are tested using simulated outbreak data based on a set of scenarios defined by varying the following: presence of direct transmission, sensitivity and specificity for observation of symptoms, values of the transmission parameters and household size distribution. Simulations are also used for understanding patterns in the distribution of household final sizes by varying the values of the transmission parameters. From the results using simulated outbreaks, DIC6 consistently indicates towards the correct model in almost all simulation scenarios and is robust across all the presented simulation scenarios. Also, the posterior estimates of the transmission parameters using DA- MCMC are fairly consistent with the values used in the simulation. The procedures presented in this thesis are for SEIR epidemic models wherein the latent period is shorter than the incubation period along with presence of asymptomatic infections. These procedures can be directly adapted to infections with similar or simpler natural history. The modelling framework is flexible and can be further extended to include components for vaccination and pathogen genetic sequence data