Robin Thompson | Searcharxiv

arXiv2026

Misspecification of the generation time distribution and its impact on Rt estimates in structured populations

Due to its ability to summarise 'real-time' epidemic behaviour, the time-dependent reproduction number, Rt, is a useful metric for tracking pathogen transmission and quantifying the effects of interventions during infectious disease outbreaks. The predominant models underlying inferred Rt trajectories are renewal equations, their success owing in part to the relatively few assumptions they require. One necessary assumption is the generation time distribution, which summarises the time periods between infections in infector-infectee transmission pairs. This distribution is typically assumed to be the same across all members of a population. In reality, however, it may vary systematically between population groups. In this study, we consider two Rt inference frameworks based on renewal equation models: one for a single, homogeneous group and another accounting for a structured population. We compare the estimates of Rt generated by the two models and investigate, both analytically and through simulations, under which conditions the conclusions drawn from these modelling paradigms differ. We also demonstrate a methodology for selecting the generation time for the one-group model that correctly encapsulates variations between different population groups; this allows us to use a renewal framework for a one-group model to infer Rt when, in fact, the population is structured. Finally, we use real epidemic data to demonstrate that practical Rt estimates can differ depending on whether the underlying model is the one-group model or the multi-group model. Our results motivate the need for rigorous collection of detailed epidemic data and consideration of differences between population groups to improve the accuracy of Rt estimates that are used to guide public health policy responses.

q-bio.PE↗

arXiv2025

The time-dependent reproduction number for epidemics in heterogeneous populations

The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case counts. These models almost invariably assume a homogeneous population. Individuals are assumed not to differ systematically in the rates at which they come into contact with others. It is also assumed that the typical time that elapses between one case and those it causes (known as the generation time distribution) does not differ across groups. But contact patterns are known to widely differ by age and according to other demographic groupings, and infection risk and transmission rates have been shown to vary across groups for a range of directly transmitted diseases. Here, we derive from first principles a renewal equation framework which accounts for these differences in transmission across groups. We use a generalisation of the classic McKendrick-von Foerster equation to handle populations structured into interacting groups. This system of partial differential equations allows us to derive a simple analytical expression for Rt which involves only group-level contact patterns and infection risks. We show that the same expression emerges from both deterministic and stochastic discrete-time versions of the model and demonstrate via simulations that our Rt expression governs the long-run fate of epidemics. Our renewal equation model provides a basis from which to account for more realistic, diverse populations in epidemiological models and opens the door to inferential approaches which use known group characteristics to estimate Rt.

q-bio.PE↗