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 on the timescale of epidemic unfolding and makes it possible the calculation of 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 on 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 on the network structure in the model and particularly the temporal structure of contacts.Author summary: When a new infectious disease outbreak starts, mathematical epidemiologists find themselves building or using mathematical models to understand its propagation, predict its future course, and recommend interventions to policy-makers. A key part of this process is the estimation of model parameters, including the generation intervals, i.e., the time taken by a primary case to infect a secondary case since its infection. Generation interval informs the duration of isolation and quarantine and provides a necessary input for the basic reproductive number estimation, which quantifies the transmission potential of the infection. However, the interpretation of the observed generation time is generally done under the assumption of a homogeneous, well-mixed population. Our work provides insight into the biases that might creep into estimates of parameters due to this assumption. We derive formulae that relate different types of commonly used generation intervals for a population with a heterogeneous contact network. These findings will inform infectious disease modellers on how the assumptions they make about the contact structure might bias the parameter estimation.