From networked SIS model to the Gompertz function

TL;DR

This paper derives a networked Gompertz function as an upper bound approximation for the SIS epidemic model on networks, demonstrating its effectiveness in modeling growth and contagion dynamics in real-world contact networks.

Contribution

It introduces a networked Gompertz function derived from the SIS model, providing a new analytical tool for epidemic modeling on networks.

Findings

The networked Gompertz function closely approximates the SIS model for large times.

It effectively fits empirical contagion data from real contact networks.

The upper bound captures complex contagion behaviors like multiple peaks.

Abstract

The Gompertz function is one of the most widely used models in the description of growth processes in many different fields. We obtain a networked version of the Gompertz function as a worst-case scenario for the exact solution to the SIS model on networks. This function is shown to be asymptotically equivalent to the classical scalar Gompertz function for sufficiently large times. It proves to be very effective both as an approximate solution of the networked SIS equation within a wide range of the parameters involved and as a fitting curve for the most diverse empirical data. As an instance, we perform some computational experiments, applying this function to the analysis of two real networks of sexual contacts. The numerical results highlight the analogies and the differences between the exact description provided by the SIS model and the upper bound solution proposed here, observing how the latter amplifies some empirically observed behaviors such as the presence of multiple and successive peaks in the contagion curve.