Despite the enormous attention given to the development of methods for efficient parameter estimation, there has been relatively little activity in the area of non- parametric inference. That is, drawing inference for the quantities which govern transmission, i) the force of infection and ii) the period during which an individual remains infectious, without making certain modelling assumptions about its (parametric) functional form or that it belongs to a certain family of parametric distributions.

In this talk I will describe a number of approaches which allow Bayesian non-parametric inference for the force of infection; namely via Gaussian Processes, Step Functions, and B-splines. I will also illustrate the proposed methodology via both simulated and real datasets and discuss how such methods can scale for large populations.

In this talk, the aim is to present some results on perturbation analysis of finite quasi-birth-death (QBD) processes as an important tool for understanding how certain parameters, inherently linked to the dynamics of the model, determine the properties of the process, as well as in predicting how small changes in the environmental conditions will modify the outcome. More concretely, we present an efficient computational approach to the perturbation analysis of finite QBD processes in terms of first passage times and hitting probabilities, the maximum level visited by the process before reaching states of a predetermined level, and stationary measures. Our results are motivated by, but not restricted to epidemic models, whence we comment on a Markovian model for the spread of two bacterial strains in a hospital ward.