Network structure induced bias in estimates of intrinsic generation times

The reproduction number is a critical measure of the severity of an infectious disease epidemic. The generation interval, defined as the time taken by an infector to create another infection from its time of infection, is crucial for estimating the basic reproduction number. However, the generation intervals observed, ‘realised generation intervals’, change over time depending on the dynamics of the epidemic. These time varying distributions are well understood for homogeneous 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 simplify this process by writing exact expressions for simple structured populations. We then use these expressions to demonstrate some previously unexplored biases in the estimation of the intrinsic generation times from the observed generation times, caused by the network structure assumed in the model and particularly the temporal structure of contacts.