event
Thursday 15 Jun 2023: Probabilistic predictions of SIS epidemics on networks based on population-level observations
Tanja Zerenner - University of Bristol
LSI Seminar Room A 14:30-15:30
The contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, also when considered on the population-level only, contain information about the underlying network. This information, in turn, can be utilized for predicting the future course of an ongoing epidemic.
A complete description of the susceptible-infected-susceptible (SIS) dynamics on a given network of N nodes corresponds to a Markov-chain over a state-space of dimension 2^N making numerical integration intractable even for modest values of N. We consider birth-and-death (BD) processes as lower dimensional surrogate models for describing epidemic dynamics at the population level, i.e., in terms of the aggregated number of infected nodes in the network over time. The BD-model is, like the exact formulation, a continuous-time Markov chain, but on a state space of dimension N+1 only in which the effect of the underlying network is described by a parametric model for the birth rates. We consider regular, Erd?s–Rényi and Barabási–Albert networks and demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty.
