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.
Highlights
By the time of this writing, the COVID-19 pandemic had reached every corner of the world
We use the event-driven simulation framework so that we can track the progression of the epidemic in both continuous time as well as the generation sizes corresponding with the branching process, which allows us to validate the theoretical distributions, as well as introduce a preliminary prediction for the expected continuous time emergence of successive generations
Temporal models of disease spread often fall in one of three categories. (i) Compartmental models that are deterministic in nature as they rely on ordinary differential equations, where uncertainty only stems from our imperfect knowledge of model parameters, rather than from the inherent randomness of disease transmission. (ii) Complicated agent-based models that lose the tractability of analytical models, which require significant amount of data to parametrize and do not produce explicit likelihood of outcomes. (iii) Time series analyses that can produce probabilistic forecasts
Summary
By the time of this writing, the COVID-19 pandemic had reached every corner of the world. To accurately model the potential outcomes of an epidemic based on limited case data, tools that capture the random nature of disease spread along with the structure of the population are required. It is possible to partition the population based on traits such as age, risk behaviors, or location and define how these partitions mix [11,12,13,14] While these approaches introduce more realistic contact behavior into a model, they fail to account for the inherently stochastic nature of disease spread; something of particular importance early in an outbreak. The generation-based PGF formalism succeeds in tracking emerging epidemic size in continuous time, by validating the PGF approach with event-driven simulations on networks This result allows us to use PGFs and early disease data to quantify epidemic risk and survival probability
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