Determining disease attributes from epidemic trajectories

TL;DR

This paper demonstrates that key infectious disease attributes, such as infectiousness over time and infection duration, can be inferred from epidemic trajectory data using stochastic modeling and regression techniques, aiding early outbreak analysis.

Contribution

It introduces a method to recover disease attributes from epidemic trajectories, including infectiousness profiles and infection durations, using an integro-differential equation approach.

Findings

Disease attributes are recoverable from epidemic trajectories.

Inversion methods work with both multi-trajectory and single-trajectory data.

Inferred infection duration and infectiousness profiles can inform outbreak understanding.

Abstract

Effective public health decisions require early reliable inference of infectious disease properties. In this paper we assess the ability to infer infectious disease attributes from population-level stochastic epidemic trajectories. In particular, we construct stochastic Kermack-McKendrick model trajectories, sample them with and without observational error, and evaluate inversions for the population mean infectiousness as a function of time since infection, the infection duration distribution, and its complementary cumulative distribution, the infection survival distribution. Based on an integro-differential equation formulation we employ a natural regression approach to fit the corresponding integral kernels and show that these disease attributes are recoverable from both multi-trajectory inversions and regularized single trajectory inversions. Moreover, we demonstrate that the infection duration distribution (or alternatively the infection survival distribution) and population mean infectiousness kernel recovered can be used to solve for the individual infectiousness profile, the infectiousness of an individual over the duration of their infection, assuming that individual infectiousness profiles are self-similar across individuals over the infection duration period. The work suggests that, aggressive monitoring of the stochastic evolution of a novel infectious disease outbreak in a single local well-mixed population can allow determination of the underlying disease attributes that characterize its spread.