Interplay of Generation Time and Spatial Structure in Epidemic Dynamics and the Reliability of Reproduction Ratio Estimates

The reproduction ratio R is a central metric for monitoring infectious disease epidemics and guiding public health interventions. It is typically inferred from population-level surveillance data, but such estimates can be biased by the spatial structure of the underlying population and by complexities in disease natural history. Here, we develop a theoretical framework to study how the distribution of the generation time (the time from primary to secondary infection) interacts with spatial network structure of the host population, to shape epidemic dynamics and the accuracy of R estimates. We show that the mean and dispersion of the generation time determine the contribution of subdominant epidemic modes, controlling the rate at which the system converges to its spatial equilibrium. Overdispersed generation times slow convergence near the epidemic threshold, whereas underdispersed distributions, common for respiratory pathogens, can markedly delay convergence at moderate and high transmissibility, producing long-lived biases in R. We evaluate the performance of an existing correction to incidence data that removes bias from spatial structure under simpified dynamical conditions. We demonstrate that it remains valid for arbitrary generation time distributions only if both mean and dispersion are accurately specified. Otherwise, substantial residual errors persist especially when R is above threshold. We extend the framework to short-lived perturbations, both exogenous (e.g., extreme weather, mass gatherings, mobility restrictions) and endogenous (e.g., behavioral changes), and show that realistic dispersions can amplify their impact on spatial distributions and prolong bias on R far beyond the perturbation. We illustrate these mechanisms through a case study of a respiratory pathogen in Spain, using colocation-based mobility data, and identify the conditions under which surveillance-derived R is reliable and when precise measurements of the generation time distribution are critical.