Limited data on infectious disease distribution exposes ambiguity in epidemic modeling choices

Abstract

Traditional disease transmission models assume that the infectious period is exponentially distributed with a recovery rate fixed in time and across individuals. This assumption provides analytical and computational advantages, however, it is often unrealistic when compared to empirical data. Current efforts in modeling nonexponentially distributed infectious periods are either limited to special cases or lead to unsolvable models. Also, the link between empirical data (the infectious period distribution) and the modeling needs (the definition of the corresponding recovery rates) lacks a clear understanding. Here we introduce a mapping of an arbitrary distribution of infectious periods into a distribution of recovery rates. Under the Markovian assumption to ensure analytical tractability, we show that the same infectious period distribution at the population level can be reproduced by two modeling schemes that we call host-based and population-based, depending on the individual response to the infection, and aggregated empirical data cannot easily discriminate the correct scheme. Besides being conceptually different, the two schemes also lead to different epidemic trajectories. Although sharing the same behavior close to the disease-free equilibrium, the host-based scheme deviates from the expected epidemic when reaching the endemic equilibrium of a susceptible-infectious-susceptible transmission model, while the population-based scheme turns out to be equivalent to assuming a homogeneous recovery rate. We show this through analytical computations and stochastic epidemic simulations on a contact network, using both generative network models and empirical contact data. It is therefore possible to reproduce heterogeneous infectious periods in network-based transmission models, however, the resulting prevalence is sensitive to the modeling choice for the interpretation of the empirically collected data on the length of the infectious period. In the absence of higher resolution data, studies should acknowledge such deviations in the epidemic predictions.