Determining disease attributes from epidemic trajectories.

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 the integro-differential equation formulation for a well-mixed closed population we employ Poisson GLM regression to find the corresponding integral kernels, and show that these disease attributes are recoverable from both multi-trajectory 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.