Predicting the diversity of early epidemic spread on networks

TL;DR

This paper develops a probabilistic framework using generating functions and simulations to predict the variability and early course of epidemics on networks, emphasizing the role of randomness over contact heterogeneity.

Contribution

It introduces a novel stochastic analysis approach that quantifies early epidemic variability and supercritical probabilities, improving upon deterministic models.

Findings

Early epidemic variability is mainly driven by stochasticity, not contact heterogeneity.

The framework predicts the probability of epidemic extinction or explosion in real time.

It enhances pandemic preparedness by providing probabilistic forecasts rather than deterministic assumptions.

Abstract

The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet also features significant variability reflecting the stochastic nature of disease spread. In this work, we reframe a stochastic branching process analysis in terms of probability generating functions and compare it to continuous time epidemic simulations on networks. In doing so, we predict the diversity of emerging epidemic courses on both homogeneous and heterogeneous networks. We show how the challenge of inferring the early course of an epidemic falls on the randomness of disease spread more so than on the heterogeneity of contact patterns. We provide an analysis which helps quantify, in real time, the probability that an epidemic goes supercritical or conversely, dies stochastically. These probabilities are often assumed to be one and zero, respectively, if the basic reproduction number, or R0, is greater than 1, ignoring the heterogeneity and randomness inherent to disease spread. This framework can give more insight into early epidemic spread by weighting standard deterministic models with likelihood to inform pandemic preparedness with probabilistic forecasts.