Network structure induced bias in estimates of intrinsic generation times.

The generation interval, defined as the time taken by an infector to create another infection from its time of infection, is a crucial quantity to be estimated during an infectious disease outbreak. It informs the timescale of the epidemic unfolding and makes it possible to calculate the basic reproductive ratio, which quantifies the transmission potential of an infection, from incidence data. While the intrinsic generation interval remains stable during an outbreak in the absence of interventions and behavioural changes, the generation intervals of successful infection events, 'realised generation intervals', change over time depending on the dynamics of the epidemic and how data are aggregated to define either the forward or the backward generation intervals. These time varying distributions are well understood for homogeneous, well-mixed populations, and can be used to infer the intrinsic generation interval distribution. For heterogeneous populations, the state-of-the-art method relies on the use of expensive network-based or agent-based simulations. We use the edge-based compartmental modelling framework to develop exact formulae for the generation time distribution of a Markovian SIR infection spreading on a heterogeneous contact network. These formulae are validated using stochastic outbreak simulations and relate backward and forward generation intervals with the intrinsic generation intervals. Finally, we use our results to demonstrate some previously unexplored biases in the estimation of the intrinsic generation times from the realised one, which could be caused by the incorrect assumptions about the network structure in the model and particularly the temporal structure of contacts.