Spreading Processes over Socio-Technical Networks with Phase-Type Transmissions

TL;DR

This paper introduces a methodology using phase-type distributions to model and analyze spreading processes over networks with arbitrary transmission times, bridging the gap between theoretical assumptions and real-world data.

Contribution

It extends existing network spreading models to incorporate phase-type distributions, enabling analysis of more realistic transmission time distributions.

Findings

The extended model captures non-exponential transmission times.

Analysis of Weibull-distributed transmission rates demonstrates the model's applicability.

The methodology provides a flexible framework for diverse spreading processes.

Abstract

Most theoretical tools available for the analysis of spreading processes over networks assume exponentially distributed transmission and recovery times. In practice, the empirical distribution of transmission times for many real spreading processes, such as the spread of web content through the Internet, are far from exponential. To bridge this gap between theory and practice, we propose a methodology to model and analyze spreading processes with arbitrary transmission times using phase-type distributions. Phase-type distributions are a family of distributions that is dense in the set of positive-valued distributions and can be used to approximate any given distributions. To illustrate our methodology, we focus on a popular model of spreading over networks: the susceptible-infected-susceptible (SIS) networked model. In the standard version of this model, individuals informed about a piece of information transmit this piece to its neighbors at an exponential rate. In this paper, we extend this model to the case of transmission rates following a phase-type distribution. Using this extended model, we analyze the dynamics of the spread based on a vectorial representations of phase-type distributions. We illustrate our results by analyzing spreading processes over networks with transmission and recovery rates following a Weibull distribution.