Uncertainty analysis of contagion processes based on a functional approach

The spread of a disease (idea or product) in a population is often hard to predict. In reality, we tend to observe only few specific realizations of the contagion process (e.g., the recent COVID-19 pandemic), therefore limited information can be obtained for predicting future similar events. In this work, we use large-scale simulations to study under different exogenous network properties the complete time course of the contagion process focusing on its unpredictability (or uncertainty). We exploit the functional nature of the data, i.e., the number of infected agents as a function of time, and propose a novel non-parametric measure of variance for functional data based on a weighted version of the depth-based central region area. This methodol-ogy is applied to the susceptible-infected-susceptible epidemiological model and the small-world networks. We find that the degree of uncer-tainty of a contagion process is a non-monotonic (increas-ing/decreasing) function of the contagion rate (the ratio between in-fectious and recovery probabilities). In particular, maximum uncertain-ty is attained at the “stable contagion threshold”, which represents the parameter conditions for which the endemic/steady state is reaching a plateau as a function of the contagion rate. The effect of the density of the net-work and the contagion rate are significant and quite similar, whereas the structure of the network, i.e., its amount of cluster-ing/randomness, has a mild effect on the contagion process.