Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach.

Traditional compartmental models of epidemic transmission often predict an initial phase of exponential growth, assuming uniform susceptibility and interaction within the population. However, empirical outbreak data frequently show early stages of sub-exponential growth in case incidences, challenging these assumptions and indicating that traditional models may not fully encompass the complexity of epidemic dynamics. This discrepancy has been addressed through models that incorporate early behavioral changes or spatial constraints within contact networks. In this paper, we propose the concept of "frailty", which represents the variability in individual susceptibility and transmission, as a more accurate approach to understanding epidemic growth. This concept shifts our understanding from a purely exponential model to a more nuanced, generalized model, depending on the level of heterogeneity captured by the frailty parameter. By incorporating this type of heterogeneity, often overlooked in traditional models, we present a novel mathematical framework. This framework enhances our understanding of how individual differences affect key epidemic metrics, including reproduction numbers, epidemic size, likelihood of stochastic extinction, impact of public health interventions, and accuracy of disease forecasts. By accounting for individual heterogeneity, our approach suggests that a more complex and detailed understanding of disease spread is necessary to accurately predict and manage outbreaks.