Exact approaches for the analysis of stochastic epidemic processes on small networks

This research work is framed within the area of modelling hospital-acquired infections. I will introduce a number of existing compartmental-based approaches for modelling the spread of (typically antibiotic resistant) bacteria in hospital settings. Mathematical models with a relatively small number of compartments can be used for representing the spread of bacteria across patients and healthcare workers (HCWs), including relevant factors such as environmental contamination. However, more complex approaches (i.e., models with a large number of compartments, or network-based representations) are needed for example when introducing spatial considerations or HCW-patient contact network structures. When looking at network-based approaches, I will show some recent work on analysing exactly these epidemic dynamics on small networks. When considering an SIR epidemic process on a network, this analytic and computational approach amounts to the analysis of the exact 3^N-states continuous-time Markov chain (CTMC), and makes special focus on algorithmic aspects and the organisation of the space of states S=(S,I,R)^N. Finally, I will present some recent results on the applicability of graph-automorphism lumping techniques in these systems.